relocating a wheel...

I have in the workshop a bracket clock with a badly worn escape wheel pinion. Surprisingly the 3rd wheel teeth do not show the normal step formed when there is this sort of wear in the pinion with which it meshes. It is mounted on a collet at the front, rather than on the pinion head. Although the collet has quite a wide head so there was potential to re-seat the wheel further back by reducing the thickness of the collet head,  I could not do so because it would have fouled on the fusee stop-nib, but and there was room to move it closer to the front plate without it fouling on anything. I decided to do this rather than turning it off the collet, and mounting it on a new one.
However, English & French clock wheel collets tend to be soft-soldered onto the arbor, and this one was no exception - so how do you move one without loosing concentricity? This is my answer...
I have an 8mm watchmakers lathe for which I have a (reasonably) 'true' 3-jaw chuck. The collet body to which it is attached is bored out down the centre. I made up a female centre on a bar of carbon steel which is a fairly tight push fit at the front end, with the rest of the bar reduced slightly so it slides down the collet and draw-bar without too much resistance, and long enough to stick out at the back end of the draw-bar.
To move the wheel I mounted it in the 3-jaw chuck with exposed end of the arbor supported in a female tail-stock and the made-up head-stock centre up against the pivot inside the body of the chuck.
With the lathe running very slowly, I warmed up the collet with a spirit lamp, maintaining a slight pressure on the bar down the centre of the headstock.  Once the arbor stopped rotating because the solder was soft and there was pressure on the ends of the arbor, I eased the tail-stock back slightly, re-clamped it and waited for the arbor to start turning again, all the while maintaining pressure on the head-stock centre.
The collet is now re-positioned with the wheel still concentric with the pivots, and meshing with an undamaged part of the escape pinion.
While the job (including making the head-stock centre) probably didn't take any less time than re-colleting the wheel would have, all parts are still original; and, of course, I now have the head-stock centre so in future this job will be a lot quicker!