Mrs Sew and Sew, thank you. It is a carbon pile rheostat; the most likely source of the popping is as you describe. No capacitors anywhere in it or the motor. But yes, I will definitely check the wiring.
Mrs Sew and Sew, and Tammi, if you read this; the link that Mrs S&S sent was to a page describing the button style foot controller. Mine is not the same on the outside, but indeed the idea is the same on the inside. So, it seems I likely have calibrated it incorrectly while re-assembling. I will take some time tonight to see if I can remedy that.
Thank you!