My custom 30 herrett barrel had a tight chamber. The rounds chambered easy but after firing, the neck was basically the same. Ran into poor accuracy and pressure spikes. After neck turning the brass, the problem went away and accuracy was good.
I had the same problem w/ a 7-08 and 6.5T/CU. After a little turning everything was fine.
I'd also say you are fine for the 30-30AI....002" after firing is plenty good since the brass will have fully expanded and sprung back when you took the measurement.
My .222RMI has a .248" chamber neck and I cut my cases to .2455" when loaded. This is on the tight side but it does not display any early pressure signs or spikes.