Getting the chuck centered on the table can take quite a bit of time.
Any runout, as long as radial can be setup up really well.
Vertical wobble? You have a problem.
Once the chuck is true (on the OD) then true up and lap the jaws. New learning curve there. OD is important so the scroll is centered.
Grind the jaws true in place with (jig rings to preload), then lap with a soft steel bar and grinding paste.
I can put something in my 3 jaw chuck, and it clocks below 0.001" once the scroll is centered by lightly tightening at each chuck hole.
I am getting on in years and have picked up a few shortcuts along the way.
Super X3. 3600rpm. Sheridan 6"x24" Lathe + more. Three ways to fix things: The right way, the other way, and maybe your way, which is possibly a faster wrong way.