I think you'd first want to find out if the mounted part runs true to the shank of the holder. I'd repeat this test a few times to see if there's a repeatable result that's within tolerance. Turn a stub, mount the holder onto it, then check for runout and wobble.
Assuming it's good so far, then you could mount the shank in a 4 jaw and measure what wobble you might be getting. If you get eccentricity, but no wobble, you then dial it in for zero runout. If you have wobble, take the four jaw apart, clean everything really well, reassemble, do the test again. You would also remove and remount the four jaw to see if you can correct the wobble that way. If you can't fix the wobble, forget the procedure.
By now you will have ruined that new Nicholson file determining if the material is soft enough to turn off with a cutting tool. If it isn't, you skip the entire procedure unless you have a toolpost grinder. If it can be turned, and you don't have a wobble problem, and you have dialled it in to eliminate eccentricity, you now proceed to turn it down to match the shank diameter, or you grind it down to match. If you've had to grind it down, you've also had to spend some time protecting the ways, etc from the grinding dust, and you've had to spend some time allowing the part to cool during the procedure. If it can be turned, you would still pay attention to how hot it's getting. Go have a coffee before you come back and turn to final matching size.
End result- diameter behind the nut is exactly the same size as, and concentric with the shank.
why dont you do it like this (as has been suggested by harry)? after all this gives you the runnout that matters.
i wondered what my "import" holder was like. so i made the following measurements:
runnout at far end/near end, rotating the holder on the stub by 120°
23/1000 mm, 8 mu
17 mu, 8 mu
9 mu, 2 mu
the same after having rotated collet by 180°:
25 mu, 7 mu
32 mu, 9 mu
21 mu, 3 mu
so i got it nearly no zero at the near end just by this. ( i suspect one half of these measurements are the bearings and the other half my breathing.)
as the collets have a runnout around 10 mu, depending on where they come from ( mine are of the regofix "precision" variety) i reckon the holder is pretty good.
if i were wanting to grind the shaft true, i would experiment with three collets of different size.
btw, why do you want to put this addapter into a r8 collet? i mean the r8 slop will still be there, right?