Well, a couple of interesting developments.
I stopped by the local camping store this weekend (awesome place) and they had some gloves up on the wall. I told the sales guy what I was after and he led me to something that looked perfect. Product is by Mountain Hardware (they make a lot of technical gear for climbers and skiers) and called "Heavyweight Power Stretch Glove". It's a thin polartec. Keeps much of it's insulating value when wet, stretch, no seams in bad places, pretty warm, light (1.5oz per pair). I think they were about $25.
After talking with my instructor about this issue, he whips out the Si-Tech rings and gloves, and the Viking rings and gloves. Shows me how to hold my hand. I squeeze into the Si-Tech, and they fit, but I have no inner glove on. And it's tight. He says these are the smaller rings. I then try on the viking. They fit! So it looks like I have my solution.
Hopefully, I'll get a chance to try them out in a couple months.