Haven't shot a .300 much but a Sims limbsaver slip on pad over the stock pad and it really took the bite out of my current .338 in a Browning Stainless Stalker. The Browning had a magna port job before I got it and between it and the good pad even guys who are afraid of it are surprised at its good manners.
What I like is that there is no muzzle jump and I can stay pretty much on target. I had the slip on pad and was looking for a longer stock. Tried the slip on pad and it solved two problems for me. I am very tall with long arms so it may not work for all.
I had a Ruger with a boat paddle in .338. I really liked a lot about it, even the boat paddle, but it did bite! I think it was the thin butt and kind of hard pad.
Had another with a 25" slightly bull barrel and a great fitting stock that allowed a great cheek weld built on a Springfield action. It weighed over 10 pounds and wasn't as tame as you might think it would be. It was a shooter, however.
Had a BAR in .338 for a while that I never thought I'd give up but I traded it for the Stalker. Might get another one someday. Great rifle. The very nature of the BAR took the bite out of it. I'd put on one of the miracle coatings, magnaport and put a sims pad on the next BAR making for one great weapon.
I'd call it a dead heat on recoil between the stock BAR and Stainless Stalker with my set up.
I prefer the 250 grainers, otherwise why bother? They do come back at you harder than the 200's.
Heck I found my Savage 110e in 30-06 to be as sharp as about any.
I think the .338 is basically an 06 on steroids if you use the bigger bullets. Close to the same trajectory with more energy at every point along its path.
Get a good pad and cheek weld and you can do it!