Not sure if the inner "O" ring of the stainless steel is the same size, but I have replaced a couple of mine (black delrin) with "Do it" brand rings. On the package it says 3/8" I.D. 1/2" O.D. I'm assuming 'inner' & 'outer' diameter? UPC# 009326401201
Anyway, I was lucky enough to come across these at a local mom & pop hardware store. Replacing the ring is a whole different story,, clamp-tweezers, paper clip, mini screwdriver and mucho' patience. It was much easier to find, than actually replace. LoL. Real pain in the..
EDIT: After re-reading your post,, I think your #7 size may be right. They seemed too large, at first, trying to replace in that inner groove of cap,, but will go in there with some patience. Does your #7 ring matchup to your snapped inner MAP ring, when held next to each other?