In the commercial world, the flange on the gear is trued up so that
the outside edge is exactly concentric and the face exactly
perpendicular to the shaft. That flange is then mated to the
propeller shaft flange which is trued up after being installed on the
shaft with the whole thing being turned in a lathe or other fixture.

Amen. For years I had an minor vibration in the auxiliary on my 36'
sailboat, which engine realignment, new cutlass bearing, and new engine
mounts didn't change. On last haulout, after a transmission swap (with
a trued output flange), the yard recommended the above procedure and
voila', vibration gone.