Doughnuts have been headed off for decades, by turning into the shoulder and fireforming. So reaming is a solution to a problem already taken care of with any normal turn.
Also, turning is not to reduce eccentricity, but to produce a set thickness. For this operation you absolutely cannot bind brass, but float it around a proper fitted mandrel.
Again, fireforming finishes this brass prep(completes the action for desired result).
Aldon, you won't find a 'better' turning SYSTEM than Sinclair offers in NT-4xxx
Sinclair Search : Reloading Equipment : Case Preparation : Neck Turning : Neck Turning Tools -
Their mandrel system would also apply to reduce the runout problems you've encountered, even without turning.