If its a toughie the best thing is to cut, no risk of melting that
If you wanna try one more time first consider this…Mount the ring
sturdily upside down ON something. Not the head but the shoulders
adjacent to it. A third hand is usual insufficient by itself, you can
use one to steady the assembly but do not rely on it for pressure.
Cut an appropriate groove in a charcoal block or something so that
the ring itself is quite immobile but the head does not touch the
block and you have flame access to the faceup position of the head.
Heat carefully and evenly inside and out until you see the solder get
close to melting. Use a sharpened steel tool to press down against
the underside of the peg(which is actually pointing up) when you hit
the melt temp.
If you’re going to replace the head with another peg mount be sure
to drill or ream the hole. Any residual solder in the old hole can
possibly interfere with hot alignment… it may shift when the old
solder flows…an annoying thing to say the least because now you
have to start all over again!