Work holding cartridge brass in a lathe chuck has been a challenge for me. The only approach I've found that will spin a neck with close to zero runout is chucking a straight-shank collet chuck in a 4-jaw. I use a straight-shank ER20, or ER25 collet chuck, itself chucked in a 4-jaw. The trick is mastering the 4-jaw; with practice it becomes 2nd nature. Having said that, some brass hops in the ER collet ready to rock, most of them don't. For the most part, it's time-consuming overall.
This is why once I have a piece trued-up, getting it turned; inside, outside or both, is desirable.
Maybe there are better, faster ways to guide eccentric work into concentricity, I'm just using what works for me.