I am getting a clunk when I reverse driving directions. I assumed that I'd find a problem with U joints or driveshaft bearing, but when I got under the car, these seemed to be solid and have no play. I also tried to exert pressure on the transmission tail shaft flange and differential pinion shaft flange, and they didn't seem to have any play, although I'm not sure the hand pressure I was exerting was sufficient to guage this.

The automatic transmission was in neutral, parking brake off, and one of the rear wheels was in the air. I could turn the driveshaft a certain amount (15-30 degrees?) before I got any rotation of the rear wheel.

Should there be any play at all when I do this?

If the answer is no, does this mean my differential is shot? (It's quite possible my rear wheel bearings need replacement, but I wouldn't think this would cause that kind of play through to the driveshaft).

What's a logical route for differential repair - rebuild or wrecker?