John, right again, nothing wrong with the RCMC.
Here's the bottom line:
The whole time, I've been testing the smoke unit on the bench with the shell off. The resistor is at 8 ohms and the thermistor is at 51K ohms (it's the new smoke unit board I put in last week). The fan motor tested fine. I played around a bit with the five wires than run between the smoke unit and the RCMC. I tightened a couple of screws on the smoke unit.
What was wrong? I still don't know, but after these last steps, the smoke unit is running fine again. I've let it run for quite a while, and it does not shut itself down. I'm thrilled to finally have the smoke back--and not to have to buy a new RCMC!--but it's a little unsatisfying that, in the end, I don't know exactly was the problem was.
In any event, thank you so much for all your help.