This is an easy problem to solve, for the mechanically inclined.
The vario-pulley is expanded (to go faster) or contracted (to go slower) by a conical plug that moves up and down inside the pulley. The plug's height (and thus the speed) is controlled by a thrust plate that contacts the plug. Changing the speed control moves the thrust plate up and down.
The standard failure is just that the plug assembly gets sticky on the motor rotor shaft it rides up and down on. Exercising extreme care, take the whole mechanism apart. Using q-tips and solvent, remove any hardened grease from the shaft and inside of the plug.
It is often useful to take #1000 or finer sandpaper and resurface the shaft, and to take a "curl" of sandpaper to the inside of the plug.
Once these steps are done and any metal glaze cleaned off, the plug should move up and down freely on its shaft. Thus, the thrust plate can once again take control of the plug and allow the vario-pulley to expand and contract as needed.
Note that even if the speed adjustment belt is broken, there is a hexnut -- accessible through a hole in the platter -- that you can use to adjust the "baseline" vario-pulley expansion to 33-1/3 exactly.
I've done the above procedure hundreds of times over the last 25+ years. It works evey time.
Best,
Fred Longworth