Update : Today I took off the front panel and all the screws,
etc, and actually got a look at the oven set switch. I had to remove 2
phillips head screws on the front of the switch to get it off the
panel. I could see into the switch a little bit through a hole, and
saw the shaft turn, but that was all I could see. I poked around at
the terminals to see if any were loose. Everything seemed to be tight,
and everything looked nice and shiny and new, surprisingly. I made
sure to touch all the connections, and jiggle all the wires on the
back of the oven set switch, and also on the thermostat, hoping to
"freshen up" any corroded or arced connections. I tested it after
reassembling it, and it was working normally again.

I'll have to use it a few more times, and see if it keeps working
properly.