Hello 01 Dually!
Look, hopefully one of the Techies will come to your rescue better than me... But I did a lot of custom work to my older 350 years ago... That rear diff is not likely to be the problem, big carrier bearings, big ring gear, huge pinion gear, that sort of thing. If your transmission is not leaking, no rear seal leak or discoloration in the fluid, the reverse clutch pack is not likely.... I would look at springs, and or calipers, it is probably something silly there. I remember years ago, I did have a caliper that the cups were a bit hard to push in, a little corrosion, possible binding up and not releasing, possible...
One more thing, there was an LSD clutch pack in most of the F-350's. If you were backing up not straight, but on a turn as it angled around, one wheel is turning more than the other, and I have seen one that made a bit of a clunk as the LSD Limited Slip Diff clutch pack broke free. But all these are vague guesses...
Hope I have been a little help.... Don't worry, it does not sound that bad and is probably something silly, but an undefined clunk one cannot here or see is a tough one to guess for anyone.... Regards, Ranger.