I own a Weatherby Mark V Sporter .340 Wby. Mag. scoped with a Pentax Lightseeker II 4-16x44 with Leupold QR mounts and rings. I have never had a problem with this set up. Pentax no longer makes the Lightseeker II, so I would now go with Zeiss Conquest 4.5-14x44.

If you handload, I have a load that has an energy of 5,822 fl/lb at the muzzle for your .338-378 Wby. Mag.

Good luck