After studying the behavior, and the way components tie together in the schematic, I realized that the bonus countdown actually wasn't working as expected.
I got confused because the bonus unit *IS* required to get the ball to reset, etc... so, in that sense it appeared to be functional. But in actuality, the reset/countdown solenoid was not triggering on its own. Once I realized this, I confirmed that the "stuck motor" would end if I manually stepped the bonus unit down: counting down the bonus has to happen before the target resets, outhole kick, etc occur.
This of course proved that all the relays worked. But triggering other relays actually got the bonus step down to work, too...! So clearly there's no hard-fault broken connection. So what was the problem?
The outhole bonus relay has a several switches... one of which directly controls the bonus unit step-down. This outhole bonus relay was working... but that lone switch was not making good contact. It took me an hour to finally confirm the problem was indeed limited to that switch...
...and another hour to fix the damn thing. Of course it would have to be a relay that's one of the most difficult to access... and not just that, but out of 7 switches connected to it, the defective one was the absolute hardest to reach of those! Then simply cleaning and adjusting it did not work. I could watch it make contact but no matter what, I had to press or hold it to make it fire.
So in the end I had to disassemble the stack and reverse one of the affected switch leaves to restore reliable contact points. For not having a spare switch of that size on hand, nor wanting to solder in that inaccessible spot (shoot, you'd have to disassemble the entire game just to get enough slack out of the wires in that spot, arrgh)... I was pretty pleased to at least be able to improvise that far.
So now, the game works as it did before!