Sounding more like belts. Possibly take up tire. The clutch that drives the take up spindle in play mode is different from FF/Rew clutch. It uses the back side of the 9.6 belt driven by the motor. If the FRM9.6 belt is stretched it will lower torque in play and stall easily. Also it sounds like your counter belt is stretched. If FF has plenty of torque then Possibly tire is fine. You won't really know until you take apart.
I wouldn't get belts from eBay. The counter belts don't seem to be as much of an issue but the main drive belts are usually too wide.
You need a FRM9.6 (main drive belt) and SCY7.0 (counter belt).
Main drive belt that will work is this one
A little tech tip for troubleshooting. While in play mode, if you press the pause button just enough to make the green pause light on the front to illuminate, it turns off auto-stop circuitry as long as the green light is lit.
^^^This should only be used for test purposes to see what is actually stopping while playing a tape. The take up spindle and counter or only the counter. If the take up is going when the counter stops, its the SCY7.0 belt....but replace both anyway. They're both worn. If the take up stops along with the counter it's main belt and possibly take up tire. It can also be an excessively slipping play drive clutch (which is adjustable) but that's another topic all in itself. I would focus on belt replacement and looking at spindle tire.
Keep in mind, that if you do this and bypass the auto-stop circuitry in this manner and the take up spindle is what is slipping, you will start to unravel your tape around the capstan. So do this at your own risk with a crappy tape for troubleshooting only.