I decided to change the wheel bearings as when I repacked them last October they were looking slightly blued and slightly scored. Fast forward several months (I know) I finally get around to ordering the parts because the primary driver of the car reported that the steering was getting a little wobbly. Naturally, being the unthinking stupidity-laden lug nut I am, I didn't bother to test drive the car, no. I put it up on jackstands and promptly tore the hubs off. I did to the 'grab the wheel and move it' test, and front to back there was no play. Top to bottom there was.

So the hubs came off and it was then I discovered the fun little eff-you that Mazda sent it's customers in the form of those wonderful hubs. So those were sent to a local shop to have the races removed and replaced. (I don't have a rotary tool to do the Mazdatrix mod).

And I got the hubs back with new races and proceeded to install the new bearings as I had learned in my auto classes at CC, and like when I repacked the bearings, since I didn't have access to linear weight scale (Really Mazda, a spec for the bearing nut was too much work to do?) I tightened the nut to seat the bearings, backed-off, and re-tightened until the rotor got harder to turn.

Threw the wheel back on, snugged down the lug nuts, and did the top-bottom test. There was still play.
So off came the wheel and the bearing cap and I found the nut was a slight bit loose for some reason. (and that the castle retainer and cotter pin were uncomfortably loose) So the nut was tightened until the rotor required more effort to turn [again] and the cap put back on and the wheel thrown back on.

There was still play.

It is at this point that I come to you, begging education and explanation as to my misstep/s, and how I may correct them. I understand that there is supposed to be a slight amount of play in the bearing top to bottom, but no so much that one may see it, right? It looks like the edge of the tire is moving about a mm back and forth.

Thank you for the time and the patience.