I just wanted to put this suggestion out there as something that folks here may not have considered... going the route of a puzzle ring for an engagement or wedding ring. It's only fair since this forum has been tempting me, after so many years of dreaming of going the puzzle ring route, of going with a solid ring instead.
Years ago (back in 2005) I found this ring on puzzlering.com & fell in love with it. I saved the photos which proved to be wise as they no longer offer it. While it is still lovely, I now think it's too big, too wide, too clunky.
Here are the 2 most similar rings they offer now: 6 Band Diamond/Ruby Puzzle Ring 6 Band Tricolor Diamond Puzzle Ring
A few months back I encountered this lovely:
But those aren't the ones that made me NEED to share puzzle rings with you... here are a few from Crystal Realm that blow me away. Emerald Marquise Puzzle Ring Marquise Swiss Blue Topaz Puzzle Ring Guinevere Puzzle Ring with Princess Cut Blue Topaz Guinevere Royale Puzzle Ring
I'm sure there are also other places to find pretty puzzle rings like these.