Thanks. The ProSport was a simplified model that didn't have speeds slower than 1/30 of a second and it omitted the multiple exposure feature.
Based on the manuals here:
The multiple exposure function looks like it only continues to rotate if the shutter button was held down. In my case the drum rotates any time the camera is on.
If the drum is manually rotated a bit while the camera is off when you turn the camera on does it recenter the drum? If it does that suggests a position sensor and that may be what mine is trying to do. I'll have to open it up and see what I can find internally. Also seems like the rubber drive wheel may be a little out of round but I'll deal with that after.
Do you recall what electronic component you replaced on yours that fixed the continually rotating drum? I might have the same problem as I'd assume the control electronics are probably pretty similar between models.