OK, just got home and checked the other battery post and it's the thicker one and would make it even worse so I didn't bother to put it in there.
I "think" what is happening is the positive center pin assembly is moving and wobbling around because I have to back it out (down) so far in order to get the KFL to set nearly flush. When I say nearly flush I'm talking about the thickness of a piece of paper. I don't like it to set to close because I don't want to scratch my pretty top cap on the Paps.

I gotta protect my baby.
When the center post assembly is loose like that it's actually moving up and down and from side to side a little inside the threaded plastic insert. So then every time I take the KFL off and on the center pin is actually turning slightly (I think). And when I take the bottom cap off to put batteries in, the KFL then becomes loose.
What I've been doing is trying not to move the KFL while I'm switching out the batteries. If it turns just the slightest bit then the bottom cap doesn't go back on all the way even though I can't see it with my naked eye. And then the next time I take the KFL off, the bottom cap becomes slightly loose.
Right now I have the inner battery post screwed almost all the way into the outer positive post (almost bottomed out) such that when the Paps is all assembled I can barley hear (if at all) the battery rattle while shaking it hard.
If this information helps, I measured both the KFL's 510 (male) from the shoulder (bottom) to the positive pin and the depth of the Paps (female) while having it adjusted for the KFL to set nearly flush.
KFL+ = 4.623 mm
Paps = 4.445 mm
Note the difference is about the thickness of a heavy piece of paper.
Do you think I could just wrap the outer threads of the center post assembly with some Teflon tape to snug it up a little inside the plastic part? I think that might work.