Now----- I am just guessing, but by using my machinist intuition, I 
would suspect 
that Meyer has, a special mouthpiece facing, lapping machine 
(osculating movement).  This machine would be 
equipped, with interchangeable form blocks, that are surfaced 
textured, with a diamond 
coating (much like diamond coated files uses for sharpening knifes).

According to my theory all the MOUTHPIECES, would be first 
manufactured to a common 
rough facing shape.  The exact shape would be finished on the lapping 
machine.  One, would have to select a form block of the proper 
curvature and length, 
(to specified length and tip size) and set this form block in place, 
on to the 
osculating lapping machine.  By some kind of holding device, or 
holding fixture, the mouthpiece would be aligned with the lapping 
block, so as to allow the  osculating lapping block to form/shape the 
finish of the facing and table. The lap would have to move in a 
perpendicular path to the mouthpiece length. I would thick that this 
process would also be down wet.

OK------My next theory would be a diamond-particle, wet-slurry 
compound, applied to a ball or barrel shaped buff, to polish out the 
chamber.

Any way, I do not think that the term "diamond" is used to denote the 
"lay" of the scratches, such as a CROSSHATCH, compared to circular or 
longitude or crossw

I was thinking Meyer's lapping was a hand operation.  It makes more 
sense that it is a machine operation.