I think the current TvZ theory of applying minimal pressure, pushing out, perhaps committing hard to an attack, but more likely trying to withstand Mutas while teching hard is a strategic loser.
Zerg is often just too big and powerful even when the Mutas are held.
My suggestions
1) Highly speculative theorycraft - perhaps small firebat/medic groups can be sent out quickly and continuously, like Zealots, to force the Zerg to invest much more heavily in defense than his own development. Perhaps 1 base 2rax acad and get the CC while harassing.
2) Small tweak to current play - I think when Terran pushes out pre-muta if he doesn't commit to an attack he should split off a harassment force and pull back with his main army. The harassment force should be as cost effective as possible, maybe firebat/medic or 1 marine or scv bunker or 2marines/2medic (etc). Firebat/medic seems to make the most sense to me since you need marines to go back and hold muta.
3) Small tweak to current play - I think when Terran pushes out pre-muta he should bring a couple SCVs. I realize minerals are tight but the bulk would be very helpful vs lings. Even if all you do is turn more larva into lings that's less drones/mutas.
4) Medium tweak, speculative - It seems bunkers are more cost-effective than turrets when you already have a group of marines. Perhaps the Muta threat can be fended off more cheaply if you start with bunkers and then add turrets as the muta count grows.
5) Small to medium tweak - Perhaps you can drip out single marines, single vultures or small firebat groups even while muta defense is happening, to force lings or pull the muta away or kill drones. If I ever got to push out with a MM group and threaten the counter-attack I'd definitely try to send some harassers ahead of the main army so even if I have to pull back at least I'd be doing something active.
Terran goes SKT then adds Tanks and more Firebats. He uses D-Matrix Firebats to bust through Dark Swarm.
I know the D-Matrix bust has been seen before, but I think there is great synergy here with Firebat/Tank which makes it hard to clean the Tank efficiently with Zerglings.
I might put a few SCVs with each Tank group to bodyblock and repair, even if I had to keep producing out of the main CC and cut into Marine production slightly.
I'd also like to see him get Restore at some point to clean Plague off Vessels and Tanks.
1. Firebats can just be held with a sunken. 2 Rax acad into cc was an old build. It can work on ladder or something but at the top levels it wont give stable results. Maybe a surprise win here and there but ultimately it will just be defended with a couple sunkens and your delayed cc will make holding mutas even harder since you will have less minerals for turrets.
2. people already split their army when they push out
3. on a smaller rush distance maybe bringing a couple scvs can be helpful -- back in the day when the maps were smaller terrans would do that. Now a days with the long rush distance you will lose more economy than the zerg. Remember, fundamentally, zergs can handle lower saturation pretty easily and can quickly replenish workers because of larva. terrans have to grow in a linear manner.
4. bunkers are definitely not cheaper than turrets. This is also something people used to do way back in the day and stopped using because it was costly/tied up too many units.
5. yeah ideally you would like to drop while muta harass is happening -- but to get tech that quick exposes you to mutas, and the mutas can intercept the dropship.
#3 I think there's a lot of value to constricting larva when he's trying to get the mutas out. I agree eventually he'll pull ahead.
#5 I wasn't thinking of drops, I was thinking of trying to sneak out the front or push a little to create space to sneak out the front. Drops are a big investment. A lone marine or vulture or whatever is a much smaller investment.