Well, when it looks hard, turn the problem on its head........
assuming you have your QCTP block set so the tool would be parallel to the spindle axis...how about....
Grip a piece of rod of same diameter as drill etc in the 4 jaw chuck. Center it up.
Remove drill from QCTP block temporarily.
Bring the crosslide and carriage etc over and adjust crosslide and QCTP block until the rod enters the QCTP block hole, or until the drill chuck will close evenly on it.
At that point you should be correctly alined with in a thou or two.
For regular use with a drill chuck, a piece of accurate rod and a close-fitting matching sleeve with OD and ID concentric would allow doing it easily.
Rod goes in chuck, sleeve in 4 jaw. Center sleeve, then adjust QCTP and crosslide until rod enters sleeve.
If you need it done to fractional tenths, this probably won't be good enough. But it will be as good as your centering job and the fit of rod and sleeve allow it to be.
The drill in tailstock should be automatically centered, or else you have some shimming and scraping work to do.
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Keep eye on ball.