I'm interested in the focus on the cylindrical register. It may not be as important as some may think.
This is my take on it.
In order to fit a chuck there has to be some clearance between the cylindrical register and the mating part of the chuck nose. Ideally a close running fit. The metal in tight contact is the screw thread (actually the rear flanks of the thread) and the flat register on the back of the chuck and correspondingly on the face of the nose.
Dings in any of these will affect the fit of the chuck. As will eccentricty of the screw thread. The cylindrical register can only impose a limit to run out as it is not a mating face (not in intimate contact).
The most likely cause of a bad fit is swarf or burrs ion the tops of the threads so that should be addressed first followed by high spots on the back mating surface and then the cylindrical register.
As I said this is my take on things and I'm happy to hear other arguments.
In addition as has be alluded to 3 jaw scroll chucks are not ever going to be that precise so one can only go so far with them.
MadMike suggests doing a turning test which will tell you nothing about the chuck fitting as it only tells you how good your headstock allignment is and to an extent the state of your spindle bearings.
regards Martin