Sounds like a duplicate to my rifle, Joe - .370" groove diameter with minimum chamber diameter and neck.
With necked down '06 cases, I can only use .365" Privi bullets, but with 8x57 RP brass formed, I can use up to .367" bullets.
Seems to me, the chamber in my rifle was .392" (.391" fired case), which was standard for most 9.3's (I think).
I also think .010" is fine for neck walls, but it is thin.
As long as the case neck can expand to allow an unfired bullet to be pushed into the fired neck, it's fine. They will all be the same, for your own loading development.
-------------------- Daryl
"a gun without hammers is like a Spaniel without ears" King George V