I need to rebuild my 37 FH. If possible, I'd like to bump up the compression, but I'm not finding any options for piston/heads to do so. I am aware of the Sharp heads, but $1500 is a bit steep. Are there any other options or should I just build back original?
You could have your heads milled. You have to be careful with how much though. Someone will let you know a safe amount you can have taken off, and the proper way to verify clearance.
Only goes back to '38, I would bet it would be similar to your '37. Look up how guys deck blocks and dome above the piston for good quench. By tightening up quench you will gain some compression and efficiency.
Do a search on the Ford Barn , lots of information on milling heads , getting the proper piston to head clearance to wake a flathead up.
Or this on the H.A.M.B. : https://www.jalopyjournal.com/forum/threads/high-compression-heads-worth-it.1273049/#post-14595485.
BEFORE YOU CUT ANYTHING, put some clay on the heads above the valves and roll the engine over. Pull the heads and measure the thickness of the clay, BEFORE YOU CUT ANYTHING. Your heads or the block may have already been milled at some time. Ask me how I know.