Bruce, I might get flamed for this!
For high precision work on small diameter spindles, machine shops use a collet instead of a chuck. A collet based mandrel has the advantage that there are only two operations needed on a shaft of the proper diameter (size D drill rod) 1. Thread the end for the nut. 2. Center drill the end for the 60 deg. live center. Of course, the edge of the opposite end can be eased, or rounded slightly for ease of insertion into the collet.
The outside of the collet itself, of course, would fit the Morse taper.
This type of mandrel, complete with collet, is availabe for about $26. I am not sure about the accuracy of the collet itself.
I use the Woodcraft $10 mandrels myself. The Morse taper has a deep hole, and the shaft threads at the end of the hole. They seem to run true, I tested mine with a dial indicator. I bought an extra shaft just in case.
Just my $.0002. Close tolerance, eh ?