If the error change with the change in cam and pin mating then the chucks isn't mounting to the camlock taper face correctly. Try blueing the face of the spindle and see how good the contact is with the backplate, correct the backplate to make it consistent. I've used Plastigage on the face of the spindle to see if I was getting 100% contact, just hold it on with a dab of grease or oil. Mark the pins with the cam numbers so that you always use the same mounts and the chuck should return to the same position on the spindle.
Once you're sure of the backplate mounting on the spindle take a pass on the face of the backplate, and a little cleaning pass on the outside to make things square and concentric. I don't worry a lot about the register being a press fit with the chuck back recess but feel free to do so yourself. It should mount cleanly, make sure that the boss on the backplate doesn't bottom out in the chuck. If you want take a little time and blue the interface between backplate and chuck back, you should have a decent and even transfer.
When you mount you can tighten up the screws a bit then knock the chuck to center if there's a little clearance in the back. A lot of chucks have the jaws ground true to the outside of the chuck so this should help bring the jaws to center.
If the jaws don't come to center after this try cleaning the insternals of the chuck, paying close attention to the fit of the scroll to the center boss - if it's loose nothing will ever center reliably. If things look good clean them up and reassemble.
If there's still error characterize the error - is it the same on the same test piece? Does it change with the side of the test piece? If it's about the same all around you could regrind the jaws, if it's all over the map the shuck was likely overstressed at some point (likely a gorilla using it) and there's not a lot you can do to fix it.
I do most of the above as a matter of course so I don't really know if it's improved any chucks. But most of my chucks can be mounted and function as I want them to immediately so something must be right.
(BTW: .002-.003 is likely in the chuck spec, if you really want something better that you can slap on and make work you'll want to investigate a draw-in chuck system such as a 5C collet chuck. If you have soft jaws or an adjust-true chuck you can make a particular diameter have a low error, but will have to adjust again when you move to something else. There are a lot of things that you can try, the above is just a summary.)