The tape was not my idea originally, but worked for me to, that s why I posted it here.
Originally I put the tape as I mentioned above, but after a couple of runs you can carefully remove the "up standing" parts of the tape using a cutter, it will make the little bearings move more freely, but still no slop.
Now the slop on the bevel was away, I focused again on the sideways play of the diff. The manual of the normal DEX stated copper-copper, the manual of the R version stated copper-iron (iron on diff ring side). With the slop gone, I noticed the extra pressure from the iron shim is not needed for my car, so I use copper-copper on all my diffs now. Again, this lets them work more freely, and so far no breakages. I also think there are less sideways forces on the big bearings with copper-copper, because those bearings showed sideways play too soon on my car as well.
Should have done these things much earlier!
