Get some new, unfired cases and mike them just ahead of the extrator groove so you can see what a factory-new case measures. Then get a 7/8" x 14 socket-head, cap screw and have a machinist bore an appropriately-sized hole through it (say .467" or .468") and you can use it for any case that uses a standard .30/06 case head. I had a machinist friend, who was also a handloader, do this for me about 25 years ago and it has worked great ever since. This will re-size any "swell" just ahead of the extractor groove but not do anything to the neck or shoulder, which could alter headspace. Then you can run them through your regular resizing die and proceed as you normally do.
I also have RCBS .30/06 small-base dies, that I bought for my Dad's 760 pump years ago, and they worked well for reloading for his pump and I have used them to load my bolt action rifles as well.
I've also used RCBS standard .280 Remington dies (not small-base) to load for a 7600 pump in .280 Remington and I've not had any problems.