I haven't noticed any abnormal play. In fact, I find the 6th gen shifter to be quite stout. That's probably why there is little-to-no aftermarket short throw shifters available for the TR6060 (I think just Hurst?). A short throw shifter was near the top of the list for every T56 trans car I've owned, but I haven't found myself wanting for one on this car. A contributor to the tiny aftermarket short throw options is also likely related to difficulty of install on the TR6060.
It is normal for there to be a small amount of play with the trans in gear. The more I think about it, I'd say 1/4" to 1/2" of slop is an expected amount.
Welcome to the forum. Great color choice and state