From the BASIL data, assuming you drone up and make an overlord at 9, the best timings to start morphing drones seem to be 0:00, 0:13-0:14, 0:21-0:22, 0:32-0:33, 0:38-0:39, then Overlord, then 0:58-0:59, 1:11-1:12, 1:24-1:25, 1:39-1:40.
I summarized the best timings data from BASIL into the following list, sorted by build order: 4 Pool 4 Zergling: Spawning Pool (0:34), Drone (0:56), Zergling (1:43) 5 Pool 4 Zergling: Drone (0:13), Spawning Pool (0:40), Zergling (1:49) 5 Pool 5 Creep Colony 4 Zergling: Drone (0:13), Spawning Pool (0:40), Drone (1:00), Creep Colony (1:13), Zergling (1:51) 5 Pool 5 Overlord 5 Zergling: Drone (0:13), Spawning Pool (0:40), Drone (1:00), Overlord (1:36), Zergling (1:49) 5 Pool 5 Zergling: Drone (0:13), Spawning Pool (0:40), Drone (1:00), Zergling (1:51) 5 Pool 6-8 Zerglings: Drone (0:13), Spawning Pool (0:40), Drone (1:00), Drone (1:12), Zergling (1:49), Zergling (1:49), Zergling (1:49), Zergling (1:50), Overlord (2:01), Zergling (2:05), Zergling (2:05), Zergling (2:20), Zergling (2:21), Zergling (2:33), Zergling (2:34), Zergling (2:47), Zergling (2:48), Zergling (3:01), Zergling (3:02), Hatchery (3:04) 7 Pool: Drone (0:13), Drone (0:26), Drone (0:34), Spawning Pool (0:51) 8 Extractor 9 Hatch 8 Pool 8 Overlord 8 Extractor 7 Creep Colony 7-12 Zerglings 13 Sunken Colony 18 Lair but a drone must have died before the hatch was placed: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Extractor (0:47), Drone (0:50), Drone (0:51), Drone (1:04), Hatchery (1:18), Spawning Pool (1:38), Drone (1:54), Overlord (2:20), Extractor (2:35), Creep Colony (2:38), Drone (2:47), Zergling (2:50), Zergling (2:51), Zergling (2:51), Zergling (2:51), Zergling (2:51), Zergling (2:51), Sunken Colony (2:57), Drone (2:59), Drone (3:02), Drone (3:08), Drone (3:16), Drone (3:28), Lair (3:31) 8 Extractor 9 Pool but a drone must have died before the pool was placed: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Extractor (0:47), Drone (0:50), Drone (0:51), Drone (1:04), Spawning Pool (1:09) 9 Extractor 9 Pool 8 Hatch but a drone must have died before the pool was placed: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Extractor (0:51), Drone (0:52), Drone (1:05), Spawning Pool (1:10), Hatchery (1:56) 9 Extractor 9 Hatch 8 Pool but a drone must have died before the hatchery was placed: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Extractor (0:51), Drone (0:52), Drone (1:05), Hatchery (1:18), Spawning Pool (1:38) 9 Hatch 9 Pool 8 Extractor: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Hatchery (1:12), Drone (1:29), Spawning Pool (1:38), Extractor (1:50), Drone (1:55), Drone (2:18), Overlord (2:25), Zergling (2:46) 9 Overlord 11 Hatch 10 Pool: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Overlord (1:06), Drone (1:11), Drone (1:24), Hatchery (1:35), Spawning Pool (1:53) 9 Overlord 11 Hatch 11 Pool: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Overlord (1:06), Drone (1:11), Drone (1:24), Hatchery (1:35), Drone (1:37), Spawning Pool (1:53) 9 Overlord 11 Pool 11 Extractor 11 Hatch 10 Zergling: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Overlord (1:06), Drone (1:11), Drone (1:24), Spawning Pool (1:28), Drone (1:35), Extractor (1:35), Drone (1:38), Hatchery (2:04), Zergling (2:38) 9 Overlord 12 Hatch 10 Pool 9 Extractor 13 Lair: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Overlord (1:06), Drone (1:11), Drone (1:24), Drone (1:37), Hatchery (1:37), Spawning Pool (1:53), Extractor (1:58), Drone (2:03), Drone (2:10), Drone (2:23), Drone (2:30), Drone (2:35), Lair (2:52) 9 Overlord 12 Hatch 11 Pool 10 Extractor 12 Lair 11 Zergling: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Overlord (1:06), Drone (1:11), Drone (1:24), Drone (1:37), Hatchery (1:37), Spawning Pool (1:53), Extractor (1:58), Drone (2:03), Drone (2:10), Drone (2:23), Lair (2:48), Zergling (3:03) 9 Overlord 12 Hatch 11 Pool 10 Extractor 12 Zergling: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Overlord (1:06), Drone (1:11), Drone (1:24), Drone (1:37), Hatchery (1:37), Spawning Pool (1:53), Extractor (1:58), Drone (2:03), Drone (2:10), Drone (2:23), Zergling (3:03) 9 Overlord 12 Hatch 11 Pool 10 Extractor 13 Lair: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Overlord (1:06), Drone (1:11), Drone (1:24), Drone (1:37), Hatchery (1:37), Spawning Pool (1:53), Extractor (1:58), Drone (2:03), Drone (2:10), Drone (2:23), Drone (2:30), Lair (2:50) 9 Overlord 12 Hatch 11 Pool 11 Extractor 12 Lair: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Overlord (1:06), Drone (1:11), Drone (1:24), Drone (1:37), Hatchery (1:37), Spawning Pool (1:53), Drone (1:58), Extractor (2:02), Drone (2:15), Drone (2:21), Lair (3:01) 9 Overlord 12 Hatch 11 Pool 12 Hatch 11 Zergling: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Overlord (1:06), Drone (1:11), Drone (1:24), Drone (1:37), Hatchery (1:37), Spawning Pool (1:53), Drone (1:58), Drone (2:06), Hatchery (2:34), Zergling (3:04) 9 Overlord 12 Hatch 12 Pool 11 Extractor 10 Zergling: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Overlord (1:06), Drone (1:11), Drone (1:24), Drone (1:37), Hatchery (1:37), Drone (1:40), Spawning Pool (1:44), Extractor (2:04), Zergling (3:15) 9 Overlord 12 Hatch 13 Pool: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Overlord (1:06), Drone (1:11), Drone (1:24), Drone (1:37), Hatchery (1:37), Drone (1:40), Drone (2:06), Spawning Pool (2:06) 9 Overlord 12 Hatch 16 Pool: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Overlord (1:06), Drone (1:11), Drone (1:24), Drone (1:37), Hatchery (1:37), Drone (1:40), Drone (2:06), Drone (2:20), Drone (2:23), Drone (2:36), Spawning Pool (2:45) 9 Overlord 12 Pool: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Overlord (1:06), Drone (1:11), Drone (1:24), Drone (1:37), Spawning Pool (1:38) 9 Overlord 13 Hatch 12 Pool: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Overlord (1:06), Drone (1:11), Drone (1:24), Drone (1:37), Drone (1:52), Hatchery (1:52), Spawning Pool (2:03) 9 Overlord 9 Extractor 10 Pool 11 Lair 11-16 Zerglings 17 Drone 18 Hydra Den 17 Overlord 18 Hydralisk: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Overlord (1:06), Extractor (1:14), Drone (1:21), Drone (1:24), Spawning Pool (1:30), Drone (1:39), Drone (1:52), Lair (2:20), Zergling (2:39), Zergling (2:39), Zergling (2:39), Zergling (2:39), Zergling (2:40), Zergling (2:40), Drone (2:48), Hydralisk Den (2:52), Overlord (3:15), Drone (3:17), Hydralisk (3:43) 9 Overlord 9 Hatch 9 Pool 9 Extractor 10 Zergling: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Overlord (1:06), Hatchery (1:20), Drone (1:30), Spawning Pool (1:33), Drone (1:43), Extractor (2:05), Drone (2:10), Drone (2:22), Zergling (2:56) 9 Overlord 9 Pool 10 Extractor 10 Zergling: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Overlord (1:06), Spawning Pool (1:14), Drone (1:31), Drone (1:31), Extractor (1:32), Drone (1:33), Zergling (2:27) 9 Overlord 9 Pool 10 Extractor 11 Hatch 10 Lair 10 Zergling: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Overlord (1:06), Spawning Pool (1:14), Drone (1:31), Drone (1:31), Extractor (1:32), Drone (1:33), Drone (1:47), Hatchery (2:06), Lair (2:27), Zergling (2:48) 9 Overlord 9 Pool 11 Extractor 11 Hatch 10 Lair 10 Zergling: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Overlord (1:06), Spawning Pool (1:14), Drone (1:31), Drone (1:31), Drone (1:35), Extractor (1:37), Drone (1:46), Hatchery (2:05), Lair (2:31), Zergling (2:47) 9 Overlord 9 Pool 12 Extractor 13 Hatch 12 Zergling: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Overlord (1:06), Spawning Pool (1:14), Drone (1:31), Drone (1:31), Drone (1:35), Drone (1:52), Extractor (1:54), Drone (2:06), Drone (2:21), Hatchery (2:22), Zergling (2:40) 9 Pool 8 Creep Colony 8 Extractor 9 Sunken Colony 9 Overlord 9-14 Zerglings 15 Lair 15-16 Zerglings 17 Drone etc: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Spawning Pool (1:01), Creep Colony (1:13), Drone (1:18), Extractor (1:31), Drone (1:34), Drone (1:47), Sunken Colony (1:54), Overlord (2:10), Zergling (2:29), Zergling (2:29), Zergling (2:29), Zergling (2:30), Zergling (2:30), Zergling (2:30), Lair (2:38), Zergling (2:43), Zergling (2:44), Drone (2:58), Drone (3:07), Drone (3:20), Spire (3:43) 9 Pool 8 Extractor 9 Overlord 9 Zergling but a drone must have died before the overlord started morphing: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Spawning Pool (1:01), Extractor (1:08), Drone (1:15), Drone (1:18), Drone (1:30), Overlord (1:49), Zergling (2:10) 9 Pool 8 Extractor 8 Overlord 8-17 Zerglings: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Spawning Pool (1:01), Extractor (1:08), Drone (1:15), Overlord (1:37), Zergling (2:10), Zergling (2:10), Zergling (2:10), Zergling (2:10), Zergling (2:10), Zergling (2:10), Zergling (2:24), Zergling (2:25), Zergling (2:38), Zergling (2:38), Zergling (2:52), Zergling (2:52), Zergling (3:09), Zergling (3:10), Zergling (3:25), Zergling (3:25), Zergling (3:38), Zergling (3:39), Hatchery (3:46) 9 Pool 8 Extractor 8 Overlord 8-17 Zerglings: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Spawning Pool (1:01), Extractor (1:08), Drone (1:15), Overlord (1:37), Zergling (2:10), Zergling (2:10), Zergling (2:10), Zergling (2:10), Zergling (2:10), Zergling (2:10), Zergling (2:24), Zergling (2:25), Zergling (2:38), Zergling (2:38), Zergling (2:52), Zergling (2:52), Zergling (3:09), Zergling (3:10), Zergling (3:25), Zergling (3:25), Zergling (3:38), Zergling (3:39), Overlord (4:01), Hatchery (4:03) 9 Pool 8 Extractor 9 Overlord 9-14 Zerglings 15 Lair: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Spawning Pool (1:01), Extractor (1:08), Drone (1:15), Drone (1:18), Overlord (1:46), Zergling (2:10), Zergling (2:10), Zergling (2:11), Zergling (2:11), Zergling (2:11), Zergling (2:12), Lair (2:12) 9 Pool 8 Extractor 9 Overlord 9 Creep Colony but a drone must have died before the overlord started morphing: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Spawning Pool (1:01), Extractor (1:08), Drone (1:15), Drone (1:18), Drone (1:30), Overlord (1:49), Creep Colony (1:58), Zergling (2:12), Zergling (2:12), Zergling (2:12), Zergling (2:12), Zergling (2:12), Zergling (2:12), Sunken Colony (2:15), Drone (2:21), Drone (2:35), Drone (2:49), Hatchery (2:52) 9 Pool 8 Extractor: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Spawning Pool (1:01), Extractor (1:08), Drone (1:15), Drone (1:18), Overlord (1:46), Zergling (2:10), Zergling (2:10), Zergling (2:11), Zergling (2:11), Zergling (2:11), Zergling (2:12), Zergling (2:25), Zergling (2:25), Lair (2:29) 9 Pool 8 Overlord 10 Extractor 10 Zergling: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Spawning Pool (1:01), Overlord (1:16), Drone (1:28), Drone (1:32), Extractor (1:34), Drone (1:39), Zergling (2:21) 9 Pool 8 Overlord 10 Hatch: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Spawning Pool (1:01), Overlord (1:16), Drone (1:28), Drone (1:32), Hatchery (1:54) 9 Pool 8 Overlord 11 Hatch 10 Zergling: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Spawning Pool (1:01), Overlord (1:16), Drone (1:28), Drone (1:32), Drone (1:39), Hatchery (1:56), Zergling (2:20) 9 Pool 8 Overlord 8 Extractor 10 Lair: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Spawning Pool (1:01), Overlord (1:16), Extractor (1:18), Drone (1:29), Drone (1:34), Drone (1:46), Lair (2:11) 9 Pool 8 Overlord 8 Extractor 8 Evolution Chamber 9-17 Zerglings: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Spawning Pool (1:01), Overlord (1:16), Extractor (1:18), Drone (1:29), Evolution Chamber (1:38), Drone (1:40), Drone (1:55), Zergling (2:21), Zergling (2:21), Zergling (2:21), Zergling (2:21), Zergling (2:25), Zergling (2:26), Zergling (2:41), Zergling (2:42), Zergling (2:54), Zergling (2:55), Zergling (3:07), Zergling (3:08), Zergling (3:21), Zergling (3:22), Zergling (3:35), Zergling (3:36), Hatchery (3:36) 9 Pool 8 Overlord 8 Extractor 9 Zergling: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Spawning Pool (1:01), Overlord (1:16), Extractor (1:18), Drone (1:29), Drone (1:34), Zergling (2:21) 9 Pool 9 Overlord 10 Hatch 9 Zergling: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Spawning Pool (1:01), Drone (1:13), Overlord (1:37), Drone (1:52), Hatchery (1:59), Zergling (2:12) 9 Pool 9 Overlord 9-14 Zerglings 15 Hatch: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Spawning Pool (1:01), Drone (1:13), Overlord (1:37), Zergling (2:10), Zergling (2:10), Zergling (2:10), Zergling (2:11), Zergling (2:11), Zergling (2:11), Hatchery (2:13) 9 Pool 9 Overlord 9 Hatch 8 Zergling: Drone (0:13), Drone (0:26), Drone (0:34), Drone (0:45), Drone (0:51), Spawning Pool (1:01), Drone (1:13), Overlord (1:37), Hatchery (1:53), Zergling (2:11)
If the timings are better than you expect, maybe one of the maps I mentioned has starting position(s) that have unusually good mining rates. More modern maps might be better, or worse.
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