Being a total simpleton, I use Jason’s method to centre the backplate on the R T.
NOT suggesting that Jason is a simpleton, far from it I just take the easiest way out.
Using a Morse Taper arbor to hold the backplate, in the lathe, I would turn a register to locate the chuck to the backplate.
Using these methods, The chuck will be centred on the backplate as accurately as possible (Ideally make the register size /size with the chuck register, so that it is a TIGHT fit) and the Morse Taper arbor in the R T will then centre the backplate on the RT.
Using a self centering 4 jaw, IMO, will produce no better concentricity than using a self centering 3 jaw; for the same reasons. That’s why I don’t use one.
There has to be clearance between each jaw and the scroll, so accuracy will depend up the accuracy/ comsistency of the scroll pitch and the jaw to scroll fit.
With the scroll having to have clearance within the chuck body as well the scroll / jaw clearances, great accuracy, or repeatability is unlikely to be good enough for your requirements.
Clearnces are like tolerances, they add up to bigger nunbers than you imagine!
The more clearances that are involved the less the chances of accurate or consistent location.
It is acknowledged that the concentricity provided by a 3 jaw will vary according to the diameter being used; i. e. varying according to the consistency of the pitch of the scroll.
If you want to centre work under the spindle, forgetting any discrepancies in the mill and it’s spindle, the technique, surely is to use the morse taper / register method to centre a 4 jaw independant chuck on the backplate, (Which hopefully is centred on the R T which, in turn, is centred under the mill spindle) and then to clock the work and bring it to centre as one normally would with a 4 jaw independant
Any innaccuracies will then be those within the R T and the mill.
On the basis of “Greater fleas have lesser fleas”, ultimately the accuracy and repeatability will depend on those of the machines used to manufacture the Mill and R T.
So where do stop? Presumably where cost /budget and acceptable accuracy coincide for each one of us.
Howard