I have not tried to Ring Thing, although I've been meaning to pick one up. I did have a Ringworm, which I sold because I found the carrier signal to be far too loud when I wasn't playing. The wave forms were really cool, though.
I would also consider the Montreal Assembly CA Ring Mod http://mtlasm.blogspot.com/p/ring-modulator.html
I have one, and the cool thing about it is that it can get fuzzy sounding, and you can purchase a light expression control, which I think sets up well for being noisy. Just wave it around to change the carrier.