Great news superfans! It was just the battery. I paid $60 some odd bucks, replaced it with (gulp) my mom and now the transmission is happy, which makes me happy, cuz besides a new Jetta TDI there isn't another car on the road I want. And I'm not even sure about the Jetta (never driven one.)
I have no idea why a low battery was making the car buck so violently, but I'm pretty sure it was killing the engine, starting up, dying, starting, etc. But I'm a novice sooo.... Who cares, it's running and it was only $60 and ten minutes work.