The .308 is easily adequet for moose, but probably not worth the trouble of convincing the guide otherwise and going on the hunt with that shadow of a doubt. If something did go wrong, it would automatically be your fault for not having "enough gun", and might become a self fulfilling prophecy. If this will be a "one time" deal going for moose, I'd get the .30-06 in the Savage, and mount an optic similar to what your other Savage rifles share. Familiarity with the platform will reduce your learning curve. A 180 NP, Speer GS, Swift A frame or Norma Oryx will do the job nicely with little guesswork or experimentation needed. Put a throw away scope on it and sell after the hunt, it will be easy to move in September or October in whitetail country. If Moose or heavy Western Game will be "a thing" for you going forward, get your choice in a .300 WM or .300 WSM and learn to shoot it well. The same 180s will work, with 200s and mono-metals also in play.
As for the effectiveness of .308 on moose, I've killed 4 with the caliber, 3 with regular 180 soft points, one with 150 gr M80 Ball from a MI state police M14 (wounded on highway/head shot, would not recommend). All were good, clean kills, one at 200 yards in a clearcut. All died with a relatively short trail. The .303 British round has probably killed more Canadian moose than all other calibers combined, with slightly inferior ballistics and bullets of softer construction than those available today.