What type of edgefinder do you use that can find the centre of a disk within tenths?
Why not use an indicator?
Are you using a jig borer with a tenth DRO?
Have you ever checked the hole in the RT after performing the milling of the disc? Perhaps that may show the same position, then you won't need to mill a piece every time.
A check to see if the hole is not concentric with the RT axis is to first find the centre with a DRO. Then index 90 degrees and check again repeat for 180 and 270 degrees. If the reading is the same at all positions then the hole is concentric with the RT axis and can then be accurately used as the reference for the centre of rotation.
I use one of these types for locating work edges:
https://www.amazon.com/edge-finder/s?k=edge+finder I have demonstrated to my self that I can repeatedly locate an edge to to .0001". To center the RT, I use the same procedure that I use to locate the center of a cylindrical boss on the mill, namely, find left side of the boss, zero x axis, find the right side of the boss and hit 1/2 function key to set x axis zero at center of cylinder. Then I repeat for y axis. This procedure totally eliminates any runout and backlash issues.
My 12" RT is semi-permanently located on my RF 30 clone. Rather than an MT taper , it has a 1" cylinder and my most used mounting fixture is a 4" 3 jaw chuck, making the center hole inaccessible. Much of the work that I did involved machining a cylindrical feature anyway. If I were inclined, I could set up a reference tooling ball on the frame of the RT and set my DRO absolute coordinates to that ball and apply an offset for the RT axis which would save me machining the cylinder. So far, I haven't been bothered.
When I use the RT in the vertical position, I can use a modified procedure to locate the the RT axis. I cut a cylinder from above, using the end of the end mill, then find the center of the y axis as above. I use a digital dial indicator to locate the top of the cylinder. Measuring the diameter with a micrometer, I can determine the vertical offset to the RT axis. I use the TTS tool holding system on the RF 30 clone and can determine my tooling offset from the dial indicator for each tool used. The dial indicator reads in tenths so my positioning is good to a couple of tenths.
My 6" RT, set up as a 4th axis on the Tormach CNC, is used as a vertical RT as it would serve as no useful function mounted horizontally. It has a 5" 3 jaw chuck for a work mounting fixture. Given that 3 jaw chucks are notorious for having runout, the above procedure is most expedient for alignment. Because it takes up too much table real estate , it is mounted only when needed and I have to go through an alignment procedure each time. There are machining work arounds on a CNC mill negating the need for an RT so I seldom have need of it.