Might end up being a clutch issue. I've never seen a clutch chatter "only" in reverse, but there's a first time for everything. Have you checked the transmission mount?
I can't remember the ratio but you can get clutch chatter in reverse and not in low gear. It's the way the chassis gets loaded while backing up, the extra ratio of reverse and the pulsing of the firing cylinders on the crank.
You sometimes see this when the disc doesn't have a marcel in it. The thin, wavy spring between the clutch materiel and the disc itself. Or an unsprung disc can do that.
The real cause of all those issues listed above is from too much plate load without a marcel or an unsprung hub or both. I run an unsprung cintered iron disc and don't have the issue of clutch chatter in either direction, but about the highest plate load I have is about 1000 pounds. If I put 2400 pounds on it, it would rattle my teeth out, and probably shake the dash right off the car.
