...I did not open up the rear drive at all. I measured the free play using the DMAN method, but without opening up the drive...
There should be no axial movement of the crowngear assembly in a properly assembled final drive. That you were able to detect measurable movement is a clear indication that something isn't right inside that drive.
With proper preload on the crowngear assembly as established by the crownwheel bearing shim, there should be absolutely no detectable axial movement.
If I follow your description above, this final drive was rebuilt during the prior ownership.
I helped to pioneer some of the DIY rebuild methods, but eventually started recommending against DIY rebuilds. There is a learning curve to doing these and many confounding variables come into play. This wouldn't be the first case of undershimming that resulted from a DIY rebuild (if that is what the problem is).
I don't follow these threads as closely as I used to, so I may have missed something. But if you find dark color lube you could have a spinning tapered roller bearing or a spinning crowngear assembly trunnion; either of those could have caused wear leading to axial play. However, on a previously rebuild drive, my first suspicion is under shimming due to measurement errors during that rebuild.
In any case, the drive needs open and inspection for the usual suspects: i.e. creeping input pinion bearing race, spinning tapered roller bearing, spinning trunnion, and rebuild with a new crownwheel bearing at a minimum. With detectable wobble, the tapered roller bearing would be very suspect for microspalling and should be replaced too...