The T 8 pictured goes around the rail several times. It does not seem to meet your original criteria.
I recently did a handout for my scout leaders on Quick Release Hitches. Thus, I looked in my handout for ones that meet your criteria of only one pass through the ring or around the rail. The Mooring Hitch (not Ashley’s, but what you now find on Animated or NetKnots), a Slipped Buntline Hitch [ABoK #1807], and the High Post Hitch [ABoK #1809]. All of the rest started out with two parts around.