I don't use the set-up like you are describing. I use an adjustable false crotch. Similar in design, except it is done on a piece of 16-strand line. I use a steel carabiner for the large ring, and I have an aluminum ring spliced into some 3/8 hollow braid.
It is better than the two-ringed device, as you can open the carabiner up to reset you line and don't have to rethread the whole thing.
There are pictures of the setup in TCIA's Treeworker from a few years ago.
TMW