The existing gudgeon screws on my old H-16 were #12 (don't know if that varied over the years). I was able to tap out the stripped holes in the backing plate to 1/4 inch (slightly larger). If you don't have any sheared screw parts still in the backing plate, you may able to do the same and avoid relocating the gudgeons.
I picked up a set of the die cast gudeons. None of my screws are stripped but I had to drill the screw holes in the gudgeon plate out to 9/32 to get the screws to line up with the holes in the boat. Even still the screw heads were so wide that they wanted to foul the ribs in the plate and wouldn't go fully home. I had to dremel the ribs a bit on both sides. Do these screws go all the way into the hull or is there some kind of baffle to separate the transom from the interior of the hull? I'm wondering if I need to seal the screws and holes with silicone or something to keep water from seeping past the threads.