Yes, shims, it's been suggested, although problematic as you say. I could make the shaft slightly shorter and then use the bolt and 'cap' to tighten the top bearing, but aren't ball bearings suppose to run with no preload?

As for tapper roller bearings, I've found out that I would need around 3.3Nm of torque for correctly preloading the bearings and this will get rid of the zero-shaft-play problem.

Regards,
dsc.