On the tooth pattern I can see where the pinion gear has made it shiny and see the pattern. What I also see is, what seems to be, is the pinion gear has actually worn into the ring gear. Is it smooth from the top of the tooth face all the way down to the the bottom of the face? Or is there a little lip on it where you could catch your fingernail on it.
From what I see of the wear pattern, pinion depth could be a little deeper and maybe better backlash. That would have to be checked after pinion depth. The wear pattern should be more centered on the face.
To me from what I see, the gears weren't set up properly, but I would need to see an actual pattern run.
Also, do the bearing caps look like they were marked prior to your removal?
Definitely a sealing problem somewhere. I would put all new axle and pinion seals in it.