Maybe my final stage resistor just happened to go bad at the same time I did my install? The fan on the AC also periodically ramps up and down without me changing anything, but that's been happening for a couple months with no battery problems until now

IMO, change the FSR. That symptom is a dead giveaway and was also the cause of my own battery drain problem. Cheap and easy fix. PM Morristown BMW and they will get the part right out to you at a very good price, or visit your local deal if you must have it today.