That is a great question, Boyd.
The way I did it was to set up the parted end of the spindle in a four jaw and steady rest on the bearing surface, and indicate the bearing portion of the spindle to under .0005 in two places (Chet wanted me to get to .0001 but I just couldn't get there). My line of thinking was that I want the bore to be as concentric with that bearing portion as possible. The parted spindle hung out a good 5" from the four jaw and without the steady I would have never gotten anywhere. I would check my run-out on the bearing portion of the spindle after every 2-3 passes of the boring bar and adjust as needed. As long as I was fairly conservative with maybe .010 d.o.c. (0.020 per pass) I could maintain concentricity. As far as the boring bar goes, stout is a subjective term to use for these little machines, but I made it as large as I could for the hole with which I was working...around .750 o.d. on the boring bar if memory serves.
I was expecting the spindle to be hardened, but I must have gotten an earlier model as I was able to part and bore the spindle with relative ease using a portable bandsaw and hss tooling. I wasn't able to part the spindle in the lathe, but my little grizzly bandsaw made short work of it. The headstock is cast iron and was also parted easily with the bandsaw.
Mike