Good news and meh news.
Good news is that my board is absolutely not fried.
Bad news is the bank of potentiometers I so painstakingly made was the problem. I tried wiring just one pot from it in with a much more conservative soldering method, and still nothing. There must be a short or something. It came down to even touching the VDD wire would shut down my core.
But I tried with a pot that was wired on its own, and it worked beautifully. So as of now, I've lost the battle, but I'm winning the war.