Ok, so here's what I did (click for big):
It's 3am and I've been awake for 21 hours figuring this out, and surprise! It works! Or it seems to, rather. I've only string up the low-E in case there were some problems to troubleshoot, which there are. The bridge pickup and claw are buzzy (I think it's a problem with a cold solder joint on the bottom of the claw, it had that problem after I'd first switched the bridge pup out.)
Other than that, series/parallel works, and each volume pot works in conjunction with it's respective pickup. The neck volume pot controls both pickups when both are on it seems, but there's something fishy about the tone pots. It seems the neck tone only wants to function in phase, and the bridge tone only wants to function out of phase, or vice versa, I'm not sure.
I'll go back in and fix the ground on the bridge tomorrow to see what I've done.
I would REALLY appreciate a critique regarding this wiring diagram.
As expected, I ran out of wire and had to resort to using huge cloth wire. There's physically no more room for anything else in there now, with all of those wires crisscrossing every direction.