Don't try to sell it piecemeal. That's where you lose money. You need to find someone who wants to buy it as a ring.
Check your local area for Estate Jewelers. Google "[city] estate jeweler" and see what comes up. Try those places (all of them). Bring all the paperwork you have (including the appraisal) with you. In bigger cities, estate jewelers are only interested if the center stone is 1K or bigger; not sure about smaller areas - it's basically not worth their time to try and sell smaller rings, because most people who buy estate pieces do so to save money on a big stone.
Is your appraisal a sale appraisal or an insurance appraisal? The fact that it's custom designed will drive the latter down (until it's old enough to be an heirloom piece) or the former up. Rationale is that no one else wants your custom design, but it's also harder to replace. Get a sale appraisal if all you have is an insurance appraisal.
I sold mine on CL for 60% of the sale appraisal value. That was after visiting 3 estate jewelers, one of whom wanted to rip me off, and one of whom gave me some really nice advice.
His advice was that it takes the average estate piece six months to sell. If I wanted to get more than the 38ish% he was offering me (my best offer), I would need to sell privately - and the bigger hurry I was in, the lower price I would bring in. If you want max value for estate jewelry, you have to be patient enough to wait for the right buyer. If time is your enemy, you will be more likely to bargain, accept low ball offers, etc. I expected to wait six months.
I was really fortunate; in my case I did get the full 60% I was seeking within a week. It was completely unexpected and I wouldn't expect anyone else to have the same experience, unfortunately. The right buyer just came along at the right time in my case.
Good luck - it's certainly an adventure.
If you do CL, they do have a nice feature where you can relist stuff without recreating the whole listing after it expires (1 week).
ETA: There are also jewelry specific sale sites, like idonowidont.com, where you can try to sell it.
For any online sale, the more pictures and information you put in your listing the better. Get a soft, new toothbrush and a tiny drop of dish soap and wash your ring very, very well with the hottest water you can stand (plug the drain), dry it using a blow dryer on hot (hot air eliminates water spots on the stone), and take photos using a macro lens/macro setting in bright, natural light. Show the ring from at least three angles (side, top, profile), on the finger, on a plain black background, framed on a flower, etc. to show it off well. Market the hell out of it.
[This message edited by Amazonia at 7:54 PM, April 7th (Monday)]