What about a good old fashioned hacksaw? With a good blade the job would be done in two shakes of a lamb's tail.
Seems to me that I would cut to 11'' with a hacksaw, face and drill a centre divot in each end.
Zero the work in a 4 jaw independant chuck for cutting the centre divots.
Mount a centre in the 4 jaw and zero it. You will have 1'' of stock to mount a drive dog.
Turn it between centres using a follow rest. Cut towards the headstock.
Avoid skim cuts, use the right tool and grind, d.o.c. and feed rate.
After reaching final diameter, remove the work from the centres, chuck in a 4 jaw and part to final length.
Please explain this, what spider?