I don't have experience with these bearings but I can offer a logical POV. I suspect that the bearings were installed incorrectly as face to face configuration. I would expect that the bearings used are meant to be installed back to back. Is this BK assembly one of a few you bought and it is the only troublemaker? Can you compare to your other BK assemblies that have no float?
I think you could press them back in as back to back configuration and then tweak the torque on the preload nut until you get just the preload you desire. Instead of pressing them in you could freeze the bearings and heat the housing for a smooth drop in and no pick up. Before doing that I suggest installing the bearings back to back onto the screw without the housing since they are already out. As you do up the preload nut by hand you should see the axial float disappear and the outer races touching. I would also check the depth of the two outer races when touching and compare it to the depth of the bore in the block and the depth of the retaining plate spigot just to ensure that your 0.13mm float is not partly due to float of the outer races. You should have some clearance between the retaining plate and the housing.