From a Trumpet player ...........

In my lathe screen I created some buttons that will capture the manually probed X and Z points and then can create a version 12 DXF
file from the points or draw the lines. Using CAD you can create curves based on the points. Mouthpiece exterior profile is easy.
The rim and end edge contours require more attention to duplicate.
So it's manual probing. I use axis MPG's to assist in touch off along with a light indicating probe. This allows control over
accuracy and location of the points ( +-0.0002" repeatability). Plus I can make custom probe tips and no compensation is
required. If auto probing is used, ie; G31 then a very slow probe rate is required ...like 1 or less ipm. Thus manual probing as it's quick and easy.
Just a thought... maybe make custom visualizers such that they match the mouthpiece being used!

I researched probing for the lathe and not much out there or you get high end and it's expensive.
Just some thought's,
RICH