Roger Head (and others),
I did exactly that when I made my version of the pincer style knurling tool based on a design by Graham Meek. That is, I incorporated the tool into the QCTP mounting as partially seen in the photo below. It makes the tool more rigid and makes for a better finish in my experience.

In this picture, the tool isn't quite finished, but you get the general idea.
The picture below better illustrates the body style.

John
Edited By John Hinkley on 18/11/2015 21:47:45