Ok, end result pending dry time, which may be considerable.. but looks like I'm as done as I'm gonna be, until springtime, when I rip the carpet up and sand the hardwoods down.
For the biggest, most concentrated stain, I ended up rubbing some Vicks Vaporub under my nose to mask the smell (saw it on a tv show, I figured if it'd work for dead bodies...) and it kinda worked, had to take breaks though cuz the vomit smell still came through, especially during scrub phase. I did the detergent/vinegar/water thing, and I've got a towel with a laden storage bin on top sopping up the excess. I'm thinking it'll probably come out cleaner than the surrounding carpet, but at least it won't be pinkish brown and stink like the devil. I'll rent a shampooer and get the rest at a later date, or just wait till springtime and lay the carpet to rest. I spot cleaned the other bits throughout the house, they weren't as bad as the big one.
The Pi, thank your mom for me.
Thanks y'all for the help. I'm freakin' glad THAT'S over with.