The kicker is modifying that bolt face but Savage does or did offer a 300 WSM
Striker so if you got one of those you would be ahead of the game there and that is the only one I would recommend using.
Also, I would fit the barrel via a Rem 700 design, get rid of the barrel lock nut design. With RUM and WSM chamberings, this ring is thinned and has been known to crack if overtightened. WHen they crack, imagine shooting the rifle with the barrel just floating in the threads!!!
Either of the chamberings you list would work fine with either of the bullets. THe 195 gr 270 and the 200 gr 7mm are so close ballistically its not really worth trying to pick one over the other.
At rifle velocities in my AMs, the 195 gr 270 seems to have a slight edge in ballistic performance.