I'm thinking you are trying to get this into nice display shape. Hopefully, you don't plan to use it for high-volume, precision machine work!
There are several different ways to rig up a temporary spin rig to polish that shaft. True it may effect the diameter, but most likely it will still clamp down enough to hold it.
I used my grinder and removed the wire brush wheel and fitted a tapered wooden block to it to insert into the column of my drill press. On the opposite end I mounted a couple of small casters to a plywood base. It wasn't pretty but it worked like a charm. came out with a nice satin finish. with a few hours of fiddling and headscratcing. Of course high polih is going to run more time, but you could get it done. It does require more heat.
As others have suggested, you could also just buy a new steel rod. Not as much fun though.

Shot of my drill press with the column that was rusted and pitted brown when I got it.