It's been a busy couple days.
New clutch kit is in, and transmission is back in the Corolla. I can shift gears and push the clutch and everything feels right.
All three transmission mounts are back in. Including my sketchy-ass welded-back-together rear transmission mount.
Driveshafts back in, front suspension back together.
Broke the 12 volt stud off the starter, drove to a U-pick scrapyard and got another one to stuff in. Brought my cordless impact and holy fuck I can't imagine going to a scrapyard without one now.
To do: buy new axle nuts I forgot to buy, find a bendy funnel to get the gear oil into the transmission because the fill hole is on the damn side of the thing, get the battery/airbox/wipers/cowl/whatever all back in the car, put it on its wheels and hope for the best.