Hmmm that does really sound very like Davidson, doesn't it?
So, I've been back through all my old images and reference stuff and have found a Davidson set shown with a ring holder... it's the only one I've seen with the other pieces, but it does make me think they are right. The image is from Wendy Duncan's former website, decoglasssouthwest.com, which vanished in c. 2011 (does anyone know if Wendy is still around? I know she was in and out of hospital a few years ago, and there's been no activity on her eBay account since 2010 either. )