The slot idea should be a last resort IMO. Only one FC cup starter has ever given me problems and I've had many. Once they start slipping, it gets worse as it chews shavings of aluminum.
Putting oil on these starters is a definite no no. Maybe carefully placed graphite powder is ok. Did they even receive any lubricant from new?
I would start with compressed air to clean out any debris before any sort of lubricant.

Ahh, if only victa had kept producing the thumblatch catcher series, they would be in better shape today!