If you like the fit and feel of your current stock, and it handles the recoil of the 338 effectively for you, I would stay the course. The 375's and 416's that I've owned have not been any worse in felt recoil than any of the 338 mags that I've fired. You've shot off sticks and have a sense of how good this works for you. There is value in that experience.
My experience is that stock fit plays a big role in field shooting and felt recoil. A well placed first shot is more important than rapid repeat shots. True quick pointing is more important than followup quick shooting.
If the current stock works for you, it might do well as your dedicated buffalo rifle. I would think the same would apply to the action of the rifle. The location and movement of the safety and bolt, the feel of the trigger and the balance, in my mind, are very important for field shooting.
Whatever your choices, shoot a bunch and have a good time.
Bfly


Be nice and work hard, you never have enough time or friends.