I spoke too soon!!
Ugh. I had the car running for an hour or so while I bled the cooling system, set the timing, TPS, and cold idle. At some point right before I restarted the car, or when I restarted it, the damn batt+brake lights came on again.
However, this time the alternator is charging in the normal-ish range, around 14.1-14.9.
I'm going to try swapping in another battery next, then who knows what else.