Sometimes when fired the firing pin stop jumps over the firing pin and the whole pistol jams up.  Could there be a problem with the firing pin plunger? something else?

This can happen with some loosely fitted firing pin stops.
Jeff Cooper had his guns slide and stop drilled and tapped, and had a small screw inserted that locked the stop in place.

In your case, I'd look on Brownell's web site and find an after market over-sized firing pin stop.

This may need a small amount of fitting, and may need to have the Series 80 slot cut in the lower right side.

An over-sized, fitted stop can't move out of position.

Another option, is to fit an over-strength firing pin spring.  This may prevent the stop from moving out of position, but the best fix, is a properly fitted stop.