If you do bugger the screw head, use a Dremel to cut away the crappy fitting and then you can get a vice grip on the screw head.
Or... remount your new support in a slightly different location and leave the old one there as a conversation piece.
Or, ahead and snap the old screws off and then you may be able to mount the new fitting in a "slightly" different spot to cover up at least one of the snapped screws.