You don't need a 4 jaw it's far quicker and more accurate to align off the bearing recesses, there is no need to even clock the drums with this method.
Chuck a lump of round bar of say half inch bigger diameter than the lead in to the drum bearing and maybe eight inches long
face and centre
Find the midpoint of the bar
Undercut say half an inch wide down to half inch diameter at this midpoint
Turn a 45 ish degree taper getting bigger towards the headstock from the midpoint
Turn a 45 ish degree taper getting bigger towards the tailstock from the midpoint
The angle is not critical nor does it need to be identical on the two halves
Do not remove the bar from the chuck until all drums are skimmed
Part off or cut at the midpoint with a hacksaw
Mount the drum between the two cones with a live or dead centre in the tailstock keeping lots of pressure on the tailstock and ensuring it is locked.
Machine the drums
If you need to machine a drum later just mount the bar in the chuck and remachine the taper, the other bar for the tailstock will not require any further machining..
If you had a four jaw chuck then a parallel turned section clocked in would be the quickest way to get the mandrel running true again.