Here is an alternative that is not as invasive a change. I took a 1/8"or 3/16" (don't remember which off hand) short aluminum rivet and pushed out the pin. You now have a better bearing surface and the antenna steel pin fits into the rivet perfectly.
Than I drilled out the center of the coil with a 1/8" or 3/16"drill. Need to do this carefully as the coil can spin. You could remove from the base if you need to.
I pressed the rivet into the coil and reassembled. Rotates much better, and my unit never has failed to start rotating on its on, even after sitting on the layout for a year unused. G