a light but sharp hit to your screwdriver (the rite size for screw head) will sometimes break screw free. Ive had very good luck with an impact driver. This is a cylinder shaped, about 6 inch long, hand held tool. One end holds a socket and the top is flat and is hit with a hammer. The blow twists the socket end as well as forces the driver head tightly to the head of the screw or nut. The twist, pressure, and vibration usually gets it done. They are not very expensive or most small engine shops might have one that you could rent. If not and all Else fails use a drill bit close to the size of the screw head and drill-cut off just enough head to remove your part. This leaves enough of the screw to use a good pair of vice grips on to twist out the rest. When installing the new part you would be better off just to Thur drill and use bolts, nuts, and a backing plate. Last but not least--if there is ANY type of core drill an oversize hole and fill with a thick mixture of resin and milled fiber, then drill the proper size in the center and counter sink it and seal the bolt and part with butyl. This will not only protect from water but gives the area compression posts for support. Its not overkill. Its peace of mind to properly do a job that will not fail. (A 1% cat. polyester or vinyle ester resin then mixed with milled fiber to "just runs off the mixing stick thickness" will work as well as expoy and save some time and money. Any of the three however will produce a quality job)
Are the teeth on the cams just worn down? Or is there slop where the cam pivots (worn down) where it's just not getting enough pressure on the rope?
