Ray, I find it odd that there is only a 1/16" contact patch in the back of the chuck. If this is true then that taper is not correctly ground. The camlock spindle taper is 7 degrees, 7 minutes, 30 seconds and the chuck taper should match that. Moreover, the chuck taper should be deeper than the spindle taper is long so that the back of the chuck touches the face of the spindle when the chuck is locked down. If all of this is not true then the problem is the chuck. You can check it with Prussian Blue as Dave said.
The other thing is that checking the run out on the back or front or side surfaces of the chuck gives you no useful information. It does not necessarily reflect the accuracy of the chuck. While we are on the subject of scroll chuck accuracy, the only realistic measure of accuracy is how it turns a work piece the first time. That is, if you take a piece of stock, say a 4" long piece of unturned 6061 and chucked it and turned it, what is the run out on the piece while it is still in place in the chuck. It should be zero and if it is not then you have a problem with the jaws or jaw guides. All scroll chucks should work this way.
Chucking up a test bar in a scroll chuck will always show run out, and the amount will vary with the diameter of the bar.
So, I suggest you remove the pins in back of the chuck and check the contact patch with Prussian Blue. If it is proper and adequate, meaning there is full contact and the chuck seats flat on the spindle face, then the fit is okay. Reinstall the studs and check for fit. There should be no gap between the spindle face and the back of the chuck. If there is then one of the studs is either not adjusted properly or there may be some damage to one of the cams in the spindle. It may require switching the stud positions to get a proper fit but if you can find it, mark the chuck to align with the mark on your spindle so you can reinstall the chuck the same way every time.