It may be that the eventual solution would be to buy a plain backplate, cut a thread to suit your lathe, screw it onto the Mandrel, face, and turn the OD to suit one of Arc Euro's Collet chucks.
If this is your chosen route, I would be inclined to have the Collet chuck to hand, before machining the register, so that the Backplate can be as tight a fit as possible to the Collet chuck.
They range in OD from 60 mm through to 125 mm depending on what size ER collet system you choose.
The register varies between 43 mm and 95 mm over the same range.
It would be worth looking at their website, which gives OD, register diameter and depth.
Collets and spanner will be extra.
HTH
Howard