I built a 7 sherman max on a tikka. As said above, If you want to run heavy cup and core I would run a 7 max on a medium action not the sherman short on a short action. If you want to run the 195s or really long copper I would have your Smith put some extra free bore in... Maybe 40 thou.
Good brass for the 7 saum isn't cheap and it can be fired accurately in a 7 max just like a lot of the ackleys. Then when you're done you have fireformed max brass. Hornady dies from sherman will run you 175.
My goal was a little different. I wanted to run a short barrel with a suppressor in light rifle so I was willing to give up some speed. But a lot of the really high speeds you see talked about with the heavies are using vv n570 which isn't temp stable and is hard to get. Rl 26 is another popular one... Super hard to find most of the time. The extreme line from hodgdon wont give you the speeds that the Alliant and VV high energy powders will produce so keep that in mind and set your expectations accordingly.
Personally if you're gonna have a rifle built... I think it makes more sense to build a sherman than a saum. Super efficient, more powder=more speed, decent barrel life, less recoil than my 7 Rem mag, and if you're already paying a Smith why not... If you can find a factory 7 saum that's obviously more cost effective, just lacking a little in performance.
As an example... I'm shooting copper 140 class in a short barrel at the speeds most guys in a 7 saum shoot cup and core in a 24" and I haven't even had a chance to try that many powders yet.