Ok, thank you all so much for your time and ideas. It turns out that I'm just a big idiot. I couldn't find whatever was smoking, almost took the dash off in my search. It took me a long time to even get to this point because I've been busy with school and work and the daylight just isn't what it is during the summer months (yet).
ANYWAY. I get out the multimeter and do some more tests. I figure I'll try to make it smoke some more with the middle panel and vent panels out so I can see where it's coming from. This means I have to jump start it again, but I wanted to see how the voltage was doing before. OH, LOOK AT THAT, the battery is at 12.3 ish volts. THAT'S WEIRD. so I touch to the engine, yup, still 12.3, so the ground is good. Maybe I should actually test the positive connection. Hmm... would you look at that, it's only giving 3 volts. So I'm a big idiot. I take off the terminal and clean it (again! I swear to god, I brushed and cleaned very thoroughly when I changed the battery), notice there was some grease which came off. Don't know how it got on there.
Starts right up when I reattach battery to terminal. I swear. to. god. I can't believe I'm so dumb.
Drive it around the next day, it stopped again. Popped the hood, cleaned the terminals again, works again. WTF. I think it must be the anti-corrosion grease I bought which came with the felt pads when I got the battery. Never been an issue before, so idk why it seems like it's an insulator now. Fun story on the picture, before I cleaned the terminals off the second time, I found I could jump the car to itself using the battery which had a poor connection.
Anyway, sorry for wasting everyone's time, but thought you deserved an update.
TL;DR: OP is an idiot and didn't clean the grease off the positive terminal of the battery when installing. It was the battery's connection the whole time.