For what little it is worth my choice for a pronghorn/deer cartridge is a 25-06. My wife also shoots one and is not bothered a bit by it's recoil. It is has a relatively flat trajectory that makes longer range shots fairly easy, however I will not shoot at game at 400 yards and beyond. I have plenty of other rifles that would work just fine for that purpose but to me the 25-06 seems just right.
Considering that your favorite cartridge is the 270 Win there is no real reason not to simply pick it. You can always use light bullets and loads for young shooters. For deer and pronghorn hunting will certainly do everything the popular 6.5 Creedmoor will do, and is more versatile for larger game.
Rifles are a matter of personal preference. Although the Savage is not my cup of tea it would probably serve you well.