It is the brass. Adjust your dies down and, resize again, then try the re-resized brass in the gun again. I promise, it will work.
The nickel brass from Winchester (for my WSM, anyway) does NOT size the same as regular brass! My die settings for regular brass and Winchester nickel are differant.
This will not help your overpressure problem, just your initial chambering problem. If the primers came out, is your bolt face burnt?