Being able to have a lathe with a large spindle is close to heaven, kinda odd statement, but having fussed with lesser machines; the thought sticks.
As you know one cannot chuck up tapered stuff too well, hence the suggestion for a tapered bushing. After all, the taper is in front of you on the actual barrel.
I could see an adjust true 6 jaw chuck being a nice thing(kinda a 6jaw faced with a 4 jaw). A set of deltronic pins or an Interapid test indicatior. Perhaps for those of us so inclined, an English bell chuck; but all in all, one uses what one has.........
The less the barrel extends from the holding mechanism(chuck, bushing) the less deflection the work will have during the light touch with a very sharp tool.
The ball shaped tool coated with valve compound is an old method..........does work if the crown is not messed up too badly.
The crown to me is the minute section that last touches the bullet upon exit. The flare etc is for looks and or protection. So if the dink on the flare does not get to the actual crown, the job can become more easy................sometimes.....