From what I understand, and correct me if I'm wrong... what you're pointing at is the linkage between the timer base and the vertical throttle arm... and you're stating that the timer base moves towards the rubber capped Spark Advance Stop screw while the engine's running (Automatically advancing the spark).
Even if a friction problem existed between the flywheel and the timer base, that type problem would not cause the problem as when the the engine runs... the flywheel rotates in a clockwise motion... the timer base advances, moves in a counter clockwise motion (a friction problem would result in a retard spark scenario).
NOTE: For a friction problem to create the problem of automatically advancing the timing, which is what is actually happening via your explanation... that engine would need to be running backwards, in a Counter Clockwise direction. Yes, that's possible as when Counter Rotating propellers first cam upon the scene... a kit was designed just exactly to convert the normal clockwise running engines to rotate counter clockwise. If this scenario was somehow stumbled across, however unlikely, I would think you'd have mentioned it... you haven't... however I feel it was worth mentioning.
For that timer base to advance towards the rubber capped stop screw... the vertical throttle arm would need to be applying pressure in that direction.
Notice the Idle Adjustment Screw in the vertical throttle arm, between the throttle arm and the metal cam... Back it away so that it is not touching its stop... not touching anything. That adjustment may have been turned in by someone, BUT, the picture does not back up that thought as... in the picture, the timer-base appears to be retarded properly and the vertical throttle arm does not appear to have any pressure applied to it. However, back that adjustment screw away from its stop anyway.
That stop screw adjustment may be your only problem, but if not.......
Loosen or remove the plate that holds the throttle cable adjustable trunion in place and adjust that trunion so that it lowers the setting of the vertical throttle arm.... with the idle stop screw NOT pressed up against anything and lowering the setting of the vertical throttle arm... that should bring the rpms down.... and if so, on a flushette, with that adjustable trunion, set the idle rpms as follows:
Long shaft..........(20") = 1000 rpm
Extra Long Shaft (25"") = 1200 rpm
At the moment, I can not think of anything else that would cause that timer base to advance on its own with the engine rotating in its normal clockwise direction.
Hopefully nobody has tinkered with the adjustment nut on that weird shaped linkage between the vertical throttle arm and the metal cam that slides against the Throttle Cam Roller (Idle Timing Adjustment), but if so... the Idle Timing will need to be reset via a timing light with the scribe mark of the Cam aligned to dead center of the Roller to whatever degree the service manual calls for via that adjustment but.