some thoughts,,,aided by the application of caffein,
a steady rest is "gonna leave a mark" no matter what, so you do procedures in certain 'order'. Just like suturing up a patient,,,gotta finish up on the insides before worrying about what the staples/stitches look like. Even the large high quality lathes that have ROLLER tipped steady rest fingers will BURNISH a mark on the surface of any barrel. When working on take offs [sign of someone too cheap to buy new] barrels,,,"I" use steel steady fingers with TEFLON tips and Lithium or Teflon grease. Fine marks left in the blueing, if any, can be touch blued. Soft finger tips will wear even when 'lubed' so frequent attention to them is needed to be sure slop has not come in. Take offs are worth working on usually when you or a buddy own the machinery and the money clock is NOT running! Take offs are for fun, experimental, and sometimes non logical projects.
IF the headstock spindle bearings are worn,,working out on the ways in a steady might be best. If headstock is that long,,,working out on the ways will be easier anyway. Perfection in my mind [?] is about a large spindle hole 12 x 36" lathe for "inside the spindle" barrel mounting.
Working on the ways:
mount barrel chamber end in dialed in chuck [4 or 6 jaw,,or TRUE AJUST chuck]. Mount muzzle end in tailstock center [bore]. Yes, it will possibly 'marr' what is now the crown lips,,it's ok.
Turn a true shank about 1.5" long on muzzle OD. Just enough to be able to mount in the chuck and get a cut all the way around what may not be a centered bore barrel.
Reverse barrel, mount newly trued muzzle end in chuck,,dial in recheck can be done [on surface of new shank next to chuck jaws.
Mount chamber end onto tailstock center. True cut OD at chamber cylinder just enough for full contact cut all perimeter [also may not have bore in center]. Cut shank and threads leaving tailstock center in bore. Then mount steady rest on the trued surface cylinder area of the chamber, back from the thread shank as far as possible [2"?]. Remove tailstock center and cut barrel face and counterbore if needed, and do chambering.
Remount tailstock in new chamber with center rest. Remove steadyrest. File finish/abrasive cloth finish steady marks[protect lathe ways with cover that won't snag in anything moving].
Turn barrel around and mount finished chamber end into chuck on largest OD [chamber]. Protect the chamber surface with paper or thin card [business card] stock. Mount muzzle on tailstock center AND steady rest. Then remove center and cut muzzle off 1/4" or so,,turn crown lips, finish muzzle cuts using only the steady rest for support.
Remove steady rest,,and SLOW turn barrel held only by chuck at chamber end [Remember, FULL contact of chuck jaws on cylindrical chamber area], and lightly finish last steady rest contact spot. CAREFUL~!-- the barrel is UNsupported at muzzle and SLOW speed is only speed used. Light contact of barrel only,,,you don't want to stress it from one side if possible - it is supported only be the full contact of the chuck jaws on large chamber end OD. You are ONLY doing final surface finish with hand held [careful!] emory paper or what ever you use to finish surface.
Barrel is finished if I, under the influence of caffein, have not missed something.
Lathes is fun.
{I'm not a real machinist,,I just play one on the internet}.