Update:
Several of the groups of 5 batteries read zero volts but each of them took a charge.
When i finished charging the string of 6 groups of 5 batteries, the overall pack read more than 38 volts. I only put 1000mah into each module.
Next I hooked up the two battery wires to a bike and.... nothing. Darkness.
So i disconnected one of the black wires running between the 5 cell modules, breaking the circuit and hopefully resetting the BMS as described in this thread.
I waited over night and the next day I reconnected the modules. I hooked the battery up to a bike and the bike turned on as normal.
A push on the throttle moved the rear wheel.
The battery is now back in the wheel, the wheel is back on the bike and I'm letting it charge over night.
Tomorrow I'll give it a ride and see how it goes.
Powell, I appreciate the offer. If this battery still doesn't work well, I'll take it apart again and test each of the cells more thoroughly for voltage and capacity. Maybe I have a bad cell or two. Popping in a new module will be a lot easier than welding in new cells.
I've always liked the design symmetry of the battery and the motor in the front and rear wheels and I'd like to keep these bikes that way. I'm aware of the benefits of Lipos and the drawbacks of so much weight in the wheels, doesn't matter, they're classics.