Piling on - great earlier suggestion about using a 45 ACP die to reduce the diameter of the cases base enough to determine if that's the problem, but keep in mind that, just like squeezing a tube of toothpaste, narrowing the base of the case that little bit is going to push the shoulder forward. You might need to run the case back into a FL die to fix the shoulder after you use a 45 ACP die to fix the base. Yeah...it shouldn't be that hard.
So...
And the answer to the question - "how does new virgin brass chamber" would be really good to know at this point. No need to hunt up 338-06, just a factory 30-06 round or new empty case would do. If it chambers fine, then neck up that new case in your 338-06 die and see if it still does.
Cheers,
Rex
