You would probably be happiest with a custom reamer, owned by you. You can discuss the freebore you want for the 6.5 bullets you are going to shoot, with the reamer grinder and the gunsmith. You can't expect the gunsmith to purchase a special reamer just for your chamber.
Personally, I think you would be much better off building a 6.5-284. Very good brass now available and a proven longrange accurate cartridge. I'd swap bolts or rifles and leave the 338 as is or build a big boomer on it. Or build a 300 WSM
on it, Norma brass is available for the WSM.
The 1:9 twist barrels are working very good with the heavier 6.5 bullets at around 2900-3100 fps.