Yep, my experience also. .003” runout in a three jaw is about what all of them do.
I had a similar experience replacing a stack of shims and having the spindle lock up. Two things will cause this: torquing down the headstock bolts/screws to much, thus pinching the bearing into the headstock. Or,,,Replacing shims with to thick a stack- again, forcing the bearing and bearing cap against the spindle.
The best solution is to yep, go buy some more shim stock- a package with multiple thicknesses is what you need. Then select the right set of thicknesses to shim to your ideal .001” clearance.
In your case, you’ve got the tolerance of the spindle down to .002” more or less. So ideally, take a 002” shim out of the stack, and replace it with a .001” shim. Thus you shrink the shim thickness to .001”, and still have a free spinning spindle. Ideal!
It’s maddening, I know. But worth doing in the long run. Once it’s set, it’s set!
Glenn