I’m not following your measurements. With 12.5” from the seat back to the wheel and 6” from the seat to the wheel, that only leaves 6.5” of seat to sit on. Doesn’t make any sense to me. I have a ‘52 3100 and It’s a little tight but not like your saying.
Maybe you could take a picture with a ruler in it and post it, so we could compare with ours?