As I was reading your predicament I was thinking to myself "just file the heads off flush when you're done with the installation" - then I got to your part about marring up the patchbox. I install inlays and other parts roughly finished, then file off the screw heads flush, scrape the seam between inlay and wood, and then do final finishing and polishing of the brass parts afterwards. One trick if you don't want to mar the brass is to put a thin layer of masking tape where the file will eventually hit the brass. When you've hit the tape, stop filing, remove the screw, then carefully file the head down that last tiny bit. Buttplates, triggerguards, and toeplates get the same treatment with the heads filed flush.
-Eric