5"-6" is too long to do in one setup. Since the middle diameter can be smaller, it would be easy to start with 1/4" rod and turn one end to your accurate 6.03mm diameter. Turn the rod around and work the other end so both ends would be fairly coaxial. Work the midsection in 1cm lengths sticking out of the headstock and step it along. Turn the last bit before the inside end (without chucking on that end, which might mar the end) and finish the midsection. I'm guessing it doesn't matter if the midsection is coaxial with the ends, but coaxiality at the two ends is important. Doing those ends on the as rolled bar (assuming that the bar is decently straight and round) before cutting the midsection would be more coaxial before you start cutting it down.
I think I may have 1/4" bar for you Tys if you take the job.
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