Check ALL of the rear suspension points, driveline, & mounts (u-bolts, links, mount points, shocks, u-joints, lug nuts, etc.) for play.
It sounds like you have excess play somewhere that is taken up slowly as you drive fwd... THEN when you reverse the loading (backing up) the play has to move in the opposite direction (thus the "clunk").
At the 50th one of the guys was hearing a "clunk" in the rear and we discovered that the upper contol arm (above the rear spring on a BugEye) bushing had migrated out of the arm, leaving about 1/4-inch of play in either direction. He couldn't hear the "clunk" (bad hearing, probably from years of open-top driving...), but his wife kept saying "What's that clunking noise?" on their 600 mile drive to LotO.
OF COURSE, it could be something nasty like a bad bearing in the rear end, or worn gears, but even a pumpkin swap is fairly easy & pumpkins in a variety of ratios are always popping up fairly cheap on eBay & Craig's.....
(Still, check all of the easy-to-access external stuff 1st!)
Hope this helps!

-Bear-