I centre my table by mounting the indicator on the table and indicating against the spindle by rotating the table. You avoid any potential issues with features at the centre of the table not being concentric that way. When setting parts in a 4 jaw on the table, I then mount the indicator to the spindle and rotate the part with the table. Pretty much my method is "rotate the table".
Your process ought to work, but sounds like a feature you're indicating off somewhere in your setup isn't quite concentric.
I use a "noga arm" with mag base and a Mitutoyo 0.0005 test indicator for pretty much everything. For spindle mount jobs, it's one of the cheap jointed arms that clamps around the nose of the spindle.
Sorry to hear about you coax!
If I had one indicator to go with , it would be a Bestest .0005 . Back in days of setting up Deckel jig bores , we used dti's with .00005 grads and we still missed on some true position specs with them .
