the 6mm is going to get case stretch more than say a jdj or ackley versions that have staighter side walls and grip the chamber better.
I don't belive you are going to get by with neck size only.and the hands on one on one aproatch
and cost of the barrels they do I would bet it is good to go but things do happen from time to time.
If I use virgin brass it load and extracts fine.
This also makes me think your chamber is fine or it would hang up at this point.
If I neck resize the brass when I relaod it is difficult to close and cock but does extract.
This your case has stretched and your head space is off and is to long =hard to close.
neck size will not due and you will need to full length size to get that shoulder back to get the proper head space. some times these have head space problems with custom barrels and they require your action to get this set corectly when building a barrel.
to much head space or a big gap will couse miss fires as the shell fits to loose or the oposite is tight and hard to close.
you didn't say you had problems with miss fires etc so I would also think your barrel to action fit and head space is good or close.
I am sending you a pm.