No shims are needed. There is something wrong with yours. There is very little play when it's built right. Are both bearings seated correctly on the top shaft? Is the plastic motor spacer mated to the transmission properly? The motor plate flush with the long screws just threaded to the edge of the motor plate?
Build the slipper assembly to the instructions making sure the slipper pads fit in the indents of the spur gear. Once it's all assembled again you should have no issues.
There would be play on the top shaft if there was no slipper assembly installed yet too.