The Winchester EW in 300 WSM is the way I'd go for everything. I found one of the stainless Classics recently and put it in the same B&C stock that comes on the EW. I ended up with the same gun, except no flutes on the barrel. I have only about $400 in the rifle. I also have one of the EW's in 308. Both are absolute tackdrivers, running 1/2 groups at 100 yards for 5 shots.
If you don't handload it will be almost as expensive as the 338 you have. But it will take any animal in North America, and with the range to take deer at 700-800 yards, if the shooter can do it. The 7mm Rem mag will have little flatter trajectory, but not enough to matter until you get beyond 600 yards. The 300 WSM will give you the option to use heavier bullets, better suited for larger game at closer ranges though. Your 338 will become expendable.
I wasn't completely sold on the WSM until after buying mine and using it. I'm a believer. The older 300 Win mag will beat it ballistically, but just by a hair. Only about 50 fps with most loads. I like 2 things about about the WSM over the belted versions. The rifles come in smaller, shorter, lighter packages and get their velocities from shorter barrels. Because the WSM cartridge burns powder more efficiently, you get 300 win mag velocities, with measurably less recoil.
I ran the numbers through one of the on-line recoil calculators and the best 180 gr loads in 8 lb rifles show the 30-06 at about 20 ft lbs of recoil, The 300 Win mag at about 26 ft. lbs and the 300 WSM at the same velocity as the 300 Win mag was 23 ft lbs. I can barely tell the difference in the 3 extra ft lbs of recoil over my 30-06. Going from 20 to 26 ft lbs is manageable to me, but I do notice it.
The other nice thing about the 300 WSM and handloading is that if you don't need the power, you can always load it down to 308 veocities and recoil levels.
If you don't handload it will be almost as expensive as the 338 you have. But it will take any animal in North America, and with the range to take deer at 700-800 yards, if the shooter can do it. The 7mm Rem mag will have little flatter trajectory, but not enough to matter until you get beyond 600 yards. The 300 WSM will give you the option to use heavier bullets, better suited for larger game at closer ranges though. Your 338 will become expendable.
I wasn't completely sold on the WSM until after buying mine and using it. I'm a believer. The older 300 Win mag will beat it ballistically, but just by a hair. Only about 50 fps with most loads. I like 2 things about about the WSM over the belted versions. The rifles come in smaller, shorter, lighter packages and get their velocities from shorter barrels. Because the WSM cartridge burns powder more efficiently, you get 300 win mag velocities, with measurably less recoil.
I ran the numbers through one of the on-line recoil calculators and the best 180 gr loads in 8 lb rifles show the 30-06 at about 20 ft lbs of recoil, The 300 Win mag at about 26 ft. lbs and the 300 WSM at the same velocity as the 300 Win mag was 23 ft lbs. I can barely tell the difference in the 3 extra ft lbs of recoil over my 30-06. Going from 20 to 26 ft lbs is manageable to me, but I do notice it.
The other nice thing about the 300 WSM and handloading is that if you don't need the power, you can always load it down to 308 veocities and recoil levels.