With a good quality drill bit the size of the shaft of the screw (just smaller than the width of the threads), you can slowly drill out the old screw and install a new on. The screws are relatively hard steel but with patients and the right speed of drill can (with practice) drill out the old ones with the trim still intact. Tip: center punch the broken screw first to keep drill bit from wandering off to its edge of broken screw. This requires a good high quality bit, one that is harder steel than the screw, and drill speed that does not burn the point of the bit. I usually have to do on an average of one a day on customer coaches and 95% of the time I am successful at not slipping off and drill out the edge of the broken screw.
Mike, RVIA & RVSA Certified Master RV Technician
Amy, Dr. Assistant - Roxie & Mei Ling, four legs each
2000 Gulf Stream Scenic Cruiser 450 hp & 1330# torque
06 Saturn Vue, 06 Chevy Z71 4x4 & 2014 Corvette Z51 M7