[346CADmen]

Have you checked you chuck? 3 jaw chucks, like any product, can be made in a variety of ways (how they work) and quality. Put a nice new dowel pin in your chuck and barely clamp down on it. Place an indicator on the tool holder and check the run out of the dowel, tighten the jaws and check again. The same? Acceptable? Also run down the pin axially to verify alignment there.
Collets can have similar issues. Especially when they are sprung or being used on over or undersized stock.
I apologize if this is below your level of experience, but perhaps others will find it useful.