New unfired 7x57 brass measured in front of the extractor grove (all purchased >10 years ago).

Remington .4645"
Winchester .467"
Norma .4675"

Nice rifles. I would put up w/a bit of a problem if they were mine & attempt to keep them original. You might consult someone who makes custom dies to see if a small base die would size the head down enough & look for the brass with the smallest head diameter.