I’ve had my machine for a couple of years now and yesterday I was shocked to discover that the top two screws holding the Z plat to the carriage were too long, leaving considerable wiggle. I found that both were tight, but bottomed out. Cutting them down solved the problem. I can’t believe that I never noticed the play. I have no idea if I mistakenly installed the wrong screws, if my kit had the wrong screws, etc.
Might be worth verifying yours is ok. Just grab the Z motor and check for play.