I'm gunna bookmark this as a first for me. Usually I blather on about nothing and I don't even understand what I wrote myself..... I tend to both write too much and too little. So thanks for that.
In some ways, the Y-axis is easier to work with because the screw is usually short enough to just hang off the table nut in free air and the entire anchor system is built into the front assembly. On a Bridgeport, the leade screw has a shoulder that bears against a bearing the bearing is held in place by a series of sleeves and a round clamp block that looks more complicated than they are. These sleeves do not provide the anchor. They are collectively designed to provide a way to have a floating adjustable index mark so the user knows how much to turn to get how many thou. It has to be loose enough to adjust and also have a way of fixing it so it doesn't move. That makes it look like it's part of the anchor system but it isn't.
The sleeve that has been highlighted in earlier diacussions serves as a transmission of clamping from the handle nut to the outer race of the bearing.
The anchor is actually the nut that holds the handle on in combination with the shaft bearing. The handle nut pulls the system together by pulling the screw shaft toward the user while pushing the sleeve which pushes on the outer race of the bearing. Thus the screw is held to one side of the bearing at the inner race by a shoulder on the leade screw, while being pulled by a sleeve system that bears against the outer race on the other side of the bearing. This should all be tight with the only play being in the bearing itself - which should be minimal because the balls are captured by the opposing forces on the two races.
Mind you, that is how it works on my Bridgeport style saddle. I can't vouch for yours, but it looks similar in many ways but has a differences too.
Here is a markup of your system:
View attachment 52408
The screw shoulder that bears on the bearing inner race from the inside of the saddle is marked A. This shoulder is pulled toward the bearing by tightening the handle nut 303. The force of the nut is transmitted through the handle 302 and parts 525 and 521 which push against the outside of the outer race of the bearing. 521 525 and the handle should all be keyed so they slide on the screw shaft allowing the handle nut 303 to pull the screw shaft tight by pushing on the outside or inside of the bearing. I can't tell which from the drawing.
Your mill uses a different method of capturing the bearing. Your bracket 526 appears to do that. So it may well be that your sleeve system is an inner to inner race system which would mean you can't adjust bearing play out of the system. No big deal though cuz that will be waaaay less backlash than the leade screw nut contributes.
So....... Try removing the handle nut, cleaning the threads, and then tightening the handle nut while you have your 300 thou gap showing. It will probably make it go away as you tighten it.
If not, your bearing may be shot or the sleeve worn down, or the bearing retension system loose, (the two screw collar 526).
That's as much as I can add from SW Ontario. I am absolutely confident that
@John Conroy can fix you up lickity split if that wasn't enough info or was incorrect.