The .338 is, in my way of thinking, the American version of the .375 H&H, or the "cartridge for the guy who wants one rifle that will do everything, even in good conditions, dangerous game.
The big reason why these rifles kick to much is because most of the guns are simply a pound or two too light. Compared to the .375, the .338 is seen to be a "small bore" cartridge, and it's always been stocked like a .30-06 more so than a dangerous game rifle.
Guy I used to work with had a .338 that just ate him up with full powder loads -- no wonder, because it weight in right around 8 pounds!
We pulled the butt plate off and bored a couple of extra holes and filled them full of No. 12 shot to add about 3/4s of a pound and mounted a Kick EEZ pad on it in place of the hard plastic plate.
That really tamed things considerably.
We also found that the action was moving just a tiny bit in the stock, basically allowing the action to get a running start and hit the stock with greatly increased force.
Rebedding with Accraglass not only solved that problem, but it also improved accuracy quite a bit.
"The gift which I am sending you is called a dog, and is in fact the most precious and valuable possession of mankind" -Theodorus Gaza
Baby Jesus cries when the fat redneck doesn't have military-grade firepower.