What could be damaging my furnace control board and/or what can I do to protect it?
To me it sounds more like bearings in the fan are going out. Or a bad electrical connection.
Surges that would cause a motor to jump around would blow just about every electronic device in the home up.
A motor that had bearing problems may spin up and when the bearings get hot start stalling or moving around.
If the motor was drawing two much current it could be damaging the board so I would not be looking at electrical surges from a service as much as for loose connections OR bearings going out.
Surge protection will not stop either problem from damaging the board.