There are 2 terminals above each chime. I figured they would be simple to reconnect 4 to the power and 4 to the passive... but no. Apparently the order in which they are connected determines whether the motor will operate, much less fire the sequenced solenoids. Before I start trying all 4096 possible different wiring combinations, I was hoping someone might have a suggestion?

Buy a new chime. LOL

You should contact someone who has rebuilt these before. One expert is Tim at rejuvenation.com . I have seen samples of his beautiful handiwork. My own Pryanco chime was introduced in 1938.
Smiles.