Gary, tapered roller bearings (which we use on the wheels) should not have end
play.  They should be set up with a certain preload.  This was my experience
on car wheel bearings (that used tapered rollers instead of ball bearings) and
numerous transmission applications.  We don't want the inner bearing race to
spin on the shaft (which it will if the pre-load is too light) since this
leads to galling between the race and the shaft.  Some bearing setups do
require freeplay or endplay.  This is not one of them.

Regards,
Ed de Chazal