Found this old thread with someone having the same problem. However they were talking about a Powerstar III and not a Super C8, and I can't make sense of what they were describing about the pivot in the worm gear support; I don't see anything like that in my Super C8.
Several posters do suggest it could be the coupling between the motor shaft and the worm gear. However, I don't think I can do anything about that, as the Allen head set screw in the coupler is just ever so slightly larger than my 1.6 mm bit; the 1.6 mm bit feels tight, but if I attempt to loosen the set screw it slips, and I don't want to round off the edges in the screw head. I'm trying to decide what to do about that. Threadlocker on the bit maybe?
In any event I did some experimentation last night. I had adjusted the two flat head screws to to center the worm gear on the 359 tooth gear better, but no luck. Periodic error still there.
I did confirm that the period of the error is exactly the worm gear's rotation period (4 minutes exactly), so that seems to rule out any sort of sticking and slipping.
However, I took the cover plate off to get a better look at the wobble while tracking Arcturus and a funny thing happened. With the cover plate off, the motor torques itself completely out of the housing until it is caught by the setting circle. In this configuration, the periodic error is almost completely eliminated! I think that this implies that it is the reaction force back on the motor, which creates a clockwise torque about the worm gear support, is what is eliminating the error. I tried to mimic this by tightening the tension spring nylon screw. I made it probably unreasonably tight; so tight that I don't want to leave it that way. It is certainly much tighter than when the unit ran perfectly prior to motor failure & replacement. However, with the cover plate on the periodic error was back, although perhaps (?) improved somewhat. So I'm at a loss for what to do with this knowledge.