Bruce- I think attempting to refinish a spindle's bearing surface would not be done in a lathe. Campagnolo had ground bearing surfaces, the center I would say was located from the ends, note the slight conical surface between the internal fixing bolt threads and the end.
Not an impossible grinding job, but the steel hardness could change quite drastically and a repair might not last very long, Teledyne with their titanium axles in the 70's had press fit bearing races placed over the ti shaft, a variation on that might be a better repair, though not economic.
John Jorgensen
Palos Verdes Ca USA