Yes, I opined that that was the technique you had in mind.
The problem I have is that initially you're not on a diameter of the hole so when you touch off, it's against a slanted surface. Same when you go to the other side. I'd want some assurance that you had actually measured the length of the chord before halving it to establish the middle.
The Osborne iteration solves this problem by iterating, each iteration bringing you closer to a diameter where you're touching off on a non-slanted surface.
There's also the problem of handling backlash. Many home shops lack DROs.
Before using your method, I would still want to see an accuracy check using a Zero-It or coaxial. I'm very pessimistic about achieving "part of a thousandth" centering error.

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