To cause this problem there can still only be two things happening: Parts that have become faulty in the use they've had, or something goes wrong during building.
Though I believe you on it you built it as per manual, I suggest you go through the process once more, and like others have suggested, don't tighten the diff fully and then loosen it. Slightly increase the pressure instead and test whether the gear can still slip between the plates or not.
I made a build thread recently with
a detailed guide for the diff. I read through all the problems, ideas and solutions and applied them to my diff build, so perhaps there's something small in there you missed?
If it still doesn't work, I'd suggest you have a good look at the remaining parts, the thrust bearing and the diff screw in particular. The diff screw's blue seal/threadlock might not be sufficient to keep the screw from becoming loose, and as such it might becomes loose the first time you put power onto it. The issues with the thrust bearing could be that it's slipping because of too much grease, the balls could be damaged, or the races.