OK, I reassembled the machine far enough to take some measurements. I get 18.5 VDC at rest (machine stopped, pedal up), 8 VDC with the pedal pressed just far enough to get the machine going, and 0 VDC at maximum speed. I tested these settings until the machine started to fail, where at rest, the voltage was 16.5 VDC. To determine if the voltage drop were caused by the foot pedal, I shut everything down and changed my meter connection. I found I could pick up one side of the foot pedal potentiometer by connecting to board connection #8. That way, when I got the machine in the failing condition again, I could pull that pin from the mains connector to see if the problem goes away. Then I tested for 30 minutes, but the machine would not fail for me. Gotta love intermittent problems.
I will test the transistor as recommended in the latest suggestion, let me know if my readings prompt any other actions, questions, etc.