After going through a few cheap Logitech mice, and digging through a bunch of closed blizzard forum threads, the issue appears to be related to the polling rate of the mouse. I bought a SteelSeries Rival 110 and lowered the polling rate in the SteelSeries Engine down to 125 Hz from 1000 Hz and the issue has disappeared.
I haven't seen this discussed much recently and figured I'd make this post for others who have been experiencing this issue.
TL;DR - get a mouse with a Mac software controller that you can manually lower the polling rate to 125 Hz.