Unfortunately 3 jaw chucks do not take well to abuse. Overtightening the chuck will cause damage to the scroll beyond what the normal wear and tear of the stuff that gets into the chuck will do. The scrolls get distorted and even the chuck its self can letting the jaws clamp up bell mouthed with short material. One thing you can do after tearing the chuck down and cleaning it is to chuck up a short piece of material and then measure from the front of the jaw to the chuck body. Unchuck the piece and remeasure. If you see a big difference then you definitely have wear issues. On the smaller chucks it should be possible to turn them into adjust true style chucks even if you have to make an adaptor plate. Also when you remove the chuck from the spindle make sure that there is no foreign matter between the mating faces and the area that locates the radially. Indicate the spindle to see how true it runs. I am assuming a threaded chuck here but you should have a short diameter that the chuck locates on IIRC
And now for the soapbox. I really don't like 3 jaw chucks for the most part. If I need to put something in a lathe chuck I would just as soon use a 4 jaw. First, they hold better. It takes a serious crash to knock the piece around in the chuck. Second, indicating the piece in is not rocket science. All it takes is a little practice and you would be surprised to find just how close you can eyeball it to start with. And third, most small lathes have far too much overhang from the bearings for my taste. Plus the bearings and shaft are too light to start with. As this is an Atlas I am assuming that they are sleeve bearings so I wonder how much internal clearance you have not that it would cause run-out
Forty plus years and I still have ten toes, ten fingers and both eyes. I must be doing something right.