From memory you were previously sent to
http://www.mymowerparts.com/about_us.php to download the Kawakasi repair manual for your engine, if not do it now.
Again from memory the maximum allowable end float ( crankshaft movement along it's axis ) is 0.005"
So if your crank is moving that far either it or the case is toast.
In any case the engine will have to come out & apart.
A couple of the engine makers usually fit thrust washers between the crank & the case & I think Kawakasi is one of them so check the parts diagrams before you pull the engine apart.
It will be either a new crank or a spacer between the crank & case to fix the problem, but in reality a replacement engine would be a lot easier.
If there is the slightest chance that you can get a warranty claim then take the whole mower back and show the dealer.