Blackcat,
I use a Jacobs drill chuck with a 3/8 inch x 24 tpi thread mounted on a 0MT arbour on my small Cowells lathe and I'm very happy with it..
However can I suggest that if using a commercially produced arbour requires you to re-cut the taper (so that the threaded end is close to the that part of the taper which fits into the tailstock) then don't bother. Assuming you don't have a taper turning attachment, the difficult part of the job is setting the lathe up to cut a well fitting taper (not so much difficult as fiddly trial and error requiring a lot of patience). Having put the effort in to cut a good fitting taper then I'd make my own arbours, in fact I'd make a lot from 5/8 and 3/4 dia steel bar (or whatever meets your needs). I'd also make some from smaller diameter silver steel for future use as extra centres.
The total cost of the material, plus the cost of a 3/8 inch x 24 tpi die, will be about the same as the commercially produced arbour.
What lathe do you have?
Steve