Tried it with Byz and I found it difficult,getting the chain to bend correctly and not distort. As you know these two weaves especially look right in really tight AR's...when you try to bend Byz the rings look like they fly out. Not good. Maybe if you do some fusing or soldering it would work.
How about trying viking knit instead? I've seen this done in a hoop and because it is actually woven wire instead of rings it holds it's shape well, and you could insert a wire through the middle.
Good luck!