Presumably you'll need to machine the material down from its current diameter anyway, so careful marking out, punching and centre drilling could well get you close enough – say to half a mm of the true centre. So long as your stock is more than say 1 mm bigger than the largest finished diameter you need, that should be fine.
Facing the ends completely is another matter – and even more so if you want to drill out the spindle at all. Can't think of an easy alternative to using a fixed steady.
If you can't just buy one (and for smaller lathes, check its maximum capacity first) it might be worth making one. Google 'DIY fixed steady' for inspiration.
A cheap but temporary bodge (for centring, at least) is to fix a block of wood solidly to the cross slide (and lock the slide!), and bore it using a tool held in a four jaw chuck, to a sliding fit on your stock. Grease it before use and use low rpm to put in the centres.
A slightly trickier version which will allow facing as well is to mount the block of wood to the lathe bed, securely but so it can still slide along when pushed by the carriage. Do this to bore it, again using a tool in the four jaw. Now you can fix this firmly to the lathe bed, mount your stock (with the other end held in the 4 jaw), put in the centres and face the ends.
But if a 7×14 lathe is 14" between centres, and the part is 300mm long, you'll be close to the machine's capacity, so double check that there's going to be enough carriage travel available even with the steady in place… also that you have enough length available to get the centre drill mounted in the tailstock (in a drill chuck, probably) with the stock in place held by the chuck…
It would certainly be a much easier job on a bigger machine.
Edited By Bikepete on 12/12/2015 13:07:32
Edited By Bikepete on 12/12/2015 13:12:29