I'm not sure that your compass will work on the right bulkhead anyway. That is sloped and doesn't work with most compasses that want to be mounted vertically. Right makes one that fits and it fit perfectly into the hole from the previous compass on our Catalina 25:
Venture Bulkhead Mount
I don't think these boats came with a factory compass (it was listed as an option on the original paperwork for my 1984 Catalina 25), so things could be different on your boat.
You can test for issues with nearby metal by holding the compass there and swinging it while comparing it to a known good compass.
A no-holes option would be to make a board that hangs down off of the companionway door handle and which holds the compass. You would put it away when done sailing. It wouldn't be kicked whenever someone goes below either. Two similar examples using hatch boards:
I can't find my favorite example, which is hanging from the handle on the companionway slider.