Okay, I'm really convinced now. Either.................
(1): There is no endplay of the rod/piston, but somehow the way you're trying to feel for it, pushing, pulling, shaking, whatever, is making it feel like there's a small motion somewhere, possibly the natural side2side of the rod on the wristpin. Or....................
(2): My favorite guess, not enough oil got splashed up to the underside of the piston in the beginning, and the piston journals for the wrist pin and/or the rod journal for it are slopped out, and the endplay is the piston jumping up and down on the wristpin and/or the rod.
NOTE: When installing the wristpin, it's best to turn the snap-ring gap 180 degrees to the journal edge's divot.