Very cool! Thanks for those photos! I've never seen one of those before! I would agree- like a RCA CPR250. Worked on dozens of those camcorders, and their ilk.
Yes, I believe the pinch roller is truly the problem provided you've ruled out the other suggestions mentioned here. I was replacing pinch rollers in that mechanism in the 90's (seemed like well earlier than should have been) and so I'm sure yours would be shot by now, as well.
I wonder if any one could recover it? I get laminator rollers recovered all the time by
http://www.rotadyne.com/rubber-manufacturing/basic-polymer-types/ but would have no idea what they could offer you.
Good luck with it!