It has nothing to do with the bearings you know. If it was you should send it back to tarort cause the motor will fail. But what your talking About is Called Harmonic Vibrations. A motor running gets repelled left or right as it turns. If the shaft can move up and down as well it creates a unrestricted vibration in a vertical plane. They make motor shim plates for this reason. You pull your C clip off the back and place a shim in and put the clip back and repeat until you have no play. But yes making sure the grub screw is held in place and lock-tited is a good start lol See banging on the shaft like that will kill your bearings life span. A press is a little less detrimental to bearings health but most will suggest using motor shims. They look like sure thing washers the size of your shaft!
I know this was six years ago, but i was wondering if you ever had any issues with this particular motor that you fixed. I read the other comment about damage to the bearing and i am curious, because one of my motors has the same issue.