I got great advice from commenter Atomicboy that it was most likely a cracked solder joint.
Since the problem just moved down the line after replacing the center opto, I figured they were probably right, so I reflowed solder on the board and LO! It works now!
No false-positives when the solenoids go off. I wish I had been able to identify which one it was, but hey, it's playing great now.
I wasted money on optos I didn't need, but they can go in the spare parts bin.
At least I didn't spend $34 on a new PCB like most everyone else who was dealing with this issue did.
I do need to get another E clip though. It's kind of scary: you are removing the PCB and taking off those little clips then... *tinkle* it has fallen... somewhere. I couldn't locate it. I reviewed every wire beneath and made sure that it wasn't somewhere shorting out something, but I will be a touch paranoid until I find it again.
Cardinal rule: Always have a white sheet beneath where you are working to make it easy to find anything that has fallen!