Snorkel Bob;
If it were me, and it recently was, I'd get a .338 Winchester magnum, and I did. Love it. Mine's a Tikka WhitetailHunter LHB. The Tikka was what was available, & when you're in the market for an above .30 caliber gun with a Left Hand Bolt, you can't be picky. The Tikka is frequently called a stripped down Sako, & that's pretty much correct. So, take the Sako, enjoy the new gun, & don't look back.
I don't find the recoil to be at all objectionable. That said, I did put a Pachmayr decelerator pad on it. I'm still in load development on it, but currently shooting 225 gr Hornady's at 2875 fps. I don't know what the recoil energy is, but don't find it to be unpleasant, let alone painful.
If you handload, take a good look at the secional density & B/C of the various bullets available for the .338's. I think you'll find that the caliber makes an excellent long-range platform, carrying much better downrange energy than the 7mm.
900F