I was thinking about that, but it seems like the prices you get are lower through the auction houses like Sotheby's except for the most exceptional stones. I think I can get $8-9,000 for it from a local dealer, if the appraiser who gave me their phone number is right. That seems likely to be what I would get from Sotheby's, so if those are the two options then might as well get the money right away.By far the best way to sell this is to get in touch with an auction house and sell it through then, good ones will take 20-33% but have a network of clients and deserve every penny you pay them.
It would likely take you 24 months to get the same money that they will get you in 6 months or less.
Also: congratulations from a doubter! Nice score, I hope you do better than expected with it.