I tried to UV this piece. But having streches as you said. I have checked some solutions but cant get any result.
Smooth Mesh > Extra Controls i unchecked do not smooth UVs --> bad result...
Map Borders > Do not smooth -- > no result.
Tweaking UVs wont help at all.

How ever i found some post saying something about changing the border of UV. But couldnt get any further with that. I attached the UV map of this object. For number 1 and 3 i am planning to make different textures. The body of the ring will be another texture. I thought this might be the best UV mapping solution for that kind of plan. What do you think about the streching and map?