So after a lot of looking, I have concluded that I'm not going to find a set of rings that fit this base, and if I do, I'm going to pay way too much for them. So I got an idea...
You can buy Picatinny rail blanks for less than $10 for 12", and they look to have enough meat to the underside of them to cut a groove in them that would slide over my weird Swedish rail. What if I cut the rail to length, cut that grove into it, and add some set screws to ensure that it stays put? Seems simple enough. Either I can find a machinist to cut the groove for me (calling all members? ) or I can do it the hard way with a drill press, Dremel, files, and a lot of elbow grease. Thoughts?
Got the best measurements I could. I'm not 100% sure about that angle though. It LOOKS like a 45 degree angle, but my math says it's a 14 degree angle. I'll look into that more tomorrow.