I would also wonder what "larger game" you're planning on using it on. How big, and also how far away? I can assume you're thinking larger than deer sized, since you already have a 7-30 Waters bbl.
I have a 16" brake'd 375 JDJ barrel, and my buddy has a 12" brake'd 375 Win barrel. The difference in recoil between the 2 is significant, even with my barrel being 4" longer. You are right, the JDJ will definitely give you more "oomph". You are able to launch heavier bullets, and make them go faster than the Win. The trade off is the recoil. I went through a few grips on my JDJ handgun until I got the one with just the right fit for my hand. Now shooting it is easier, and I can let her rip at the range until I run out of ammo. I couldn't do that with the factory grips I've tried. Grip fit is more important when the recoil level goes up. Same thing will apply for a carbine butt stock.
I have several carbine barrels, but nothing in a larger bore. The nice thing about the carbine's is they are super light weight, and a joy to carry around. You will hardly know it's there, until you fire it. I'm not sure how recoil tolerant you are, but a 6 pound 375 JDJ carbine may be more "fun" than you're wanting on your shoulder. Maybe you're planning on a muzzle brake? It's going to whack you some. I've been tempted to try mine on my carbine frame, but I would want a better fitting butt stock first, and a rifle scope that sits plenty forward in the rings. All I have now is the factory wood butt stock, which is too short, and not near enough comb height for looking through a scope. Not a good combination for a kicking caliber. Also, I'd go with the Warne (I believe) picatinny rail base and rings, both for strength and to be able to set the scope farther forward. I'm using the Burris dual dovetail setup on my other carbine barrels, which put the scope a bit too far back. It's not really an issue with the small calibers, but would be, I'm sure with the JDJ. I would probably go with a 22-24" full bull carbine barrel, and start it off without a brake and see how she goes.
I would think a 220 gr bullet from a 375 Win barrel would be good on elk sized critters to maybe 200 yards if you picked your shot and stayed out of the shoulder joint. I would probably limit myself to 150 yards with that combo. I wouldn't hesitate to put a 270 gr Hornady spire point through an elks shoulder out to 300 yards from the JDJ. My barrel prefers the Hornady bullet to either the 300 Sierra, or the 270 Speer.
Here's my favorite load, 5 shots fired from a rest, at 100 yards:
I think that's pretty decent for a fixed 3x TC handgun scope, and my eyesight.