Oliver,
What is the intended purpose of this rifle? You may have more than enough gun already. Believe me, if you have enough rifle to do what you want and the recoil doesn't bother you, believe me, that's the perfect situation. You don't want to be in a situation where the rifle needed recoils enough to make it difficult to shoot accurately.
I have a 300 Win. Mag., a 280 AI, a 6.5-284, and a 6BRX. And for all around hunting in South Texas (hogs, javalinas, coyotes, does, cull bucks, etc) the 6BRX with 105 gr. bullets gets the nod most of the time because of the lack of recoil, much more fun to shoot. But if I'm going after white tail trophies the 280 AI in case of a long shot. If going after elk, the 300 Win. Mag. is the ticket. What I'm saying is that I never expose myself to more recoil than necessary just because I know I can shoot a light recoiling rifle better.
Also, is this a factory barrel? I don't know that I would spend the time and money rechambering a factory barrel. If I were you, I would pull off the factory barrel and sell it, then I would look into getting a new barrel and then you can have whatever you want. 338 Federal or 284 Winchester would be nice. 260 or 7mm-08 are also great cartridges but lack the recoil that you desire. These are all on your bolt face, if you want to modify that too, then you can have a "Short Magnum" built of whatever flavor you want.
Just my $.02
-X3M