Posi rearend
 

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I've never heard of anyone having this problem in reverse only. I would start with the brakes first since it's the easiest to check out. Does your posi unit require the special friction lube? I've heard units make noises without the right lube in them, but it was never just in reverse.

Make sure you have clearance for the GV/Floorpan. In reverse you may be "raising" the rear of the trans/od assembly and hitting the floor. I'd check the rear mount too.