Thanks all again for the input.
First of all let me say that I have no complaints about the service from Arc Euro.
There are four mechanical components involved here – the backplate collet holder, nut and collet. Three of those came from Arc Euro one I made myself. Then there is a human component (me) of course. The reason for posting here was twofold: firstly to seek some help to narrow down the problem (successfully I think) and secondly to try to gauge what level of accuracy it would be reasonable to expect from the Arc Euro products.
I do really need to make this work – the price of the stuff from Arc Euro is a fairly small consideration compared to the investment of time to make the backplate.
The people telling me to do the nut up more tightly seem to be spot on. Now that I've hunted down a big enough spanner and tightened the thing up the runout has reduced to less than a thou. The runout seems to be slightly less with the 3mm Proxxon cutter shank than it does with the 3.2mm drill. This is a good result – now it is worth my while to chase down the half a thou of runout that I measured inside the collet holder taper.
I do still think that I might want to replace the nut even if it is perfect. The spanner needed to do the thing up is nearly as big as the lathe and hardly convenient to store with the lathe tooling. A nut that uses one of those pegged wrench things seems like a better bet.
For the people who asked… my backplate started out as a piece of 60mm diameter by 20mm long cast iron bar from College Engineering. Most of the machining was done on my Cowells lathe with just the final few ops done on the Unimat. I don't think the Unimat has enough slow speed torque for this job and holding that diameter would also be a challenge. The collet holder is 62mm diameter so I needed to be careful to keep as much of the diameter of the blank bar as possible to provide enough 'meat' for the three M5 fixing screw threads but I think that going up to 70mm bar would have made life tricky on the Cowells.
Finally… I'm no expert machinist but I do have an engineering background… sufficient to know that there is no such thing as perfect. Everything has an error and each part that is added will usually make the cumulative error worse. It would still be useful to see runout measurements from other people with the same (or more high end) collet setups… what is a reasonable expectation for runout from the Arc Euro products and what (if any) improvement is obtainable for more money?
Regards, Andy