In an attempt to diagnose the problem, I rigged up a circuit tied in to the lines going to the two solenoids near the top of the transmission that shift the tranny into lockup. (I actually know something about electronics, as opposed to automotive stuff.) And I was out driving around at night so I could see whether the LEDs were blinking. But, the expected signals weren't being sent to the solenoids. Actually that was good news because it meant there probably wasn't anything wrong with the transmission.
It was at that point that someone suggested it might be a temperature problem - possibly a bad thermostat, or air that hadn't been bled out. So I tried the air bleed, and the tranny worked perfectly after that.
By the way, the proper signals going to the solenoids turned out to be a bit strange. One gets a solid 12V, but the other one gets a pulsing signal - modulated in some way.