Mike's suggestion on the .38/55 is the best one, in my humble opinion. After shooting a .375 Winchester for a while, and taking 2 moose with it's little 220gr. bullets loaded to .38/55 specs, I'd have to agree that it is a superb deer/moose/blackbear round, within it's range limitations. Pressure need not be over 35,000cup, velocities aorund 1,900fps and it'll drop deer, moose and bear as quickly or more quickly than the little ctgs. The 220 gr. Hornady is a wonderful bullet for that velocity range. In a stronger action like a #1, of course, it can be cranked up considerably.
: .356 Winchester is another great round just about duplicating the .358 Winchester from bolt guns. It'll work for deer, bear, moose, elk and big bears as well, depending on the load and bullet weight used.
: Breech pressure is what you make it.
: For a break-open rifle as you stated, HomemadeDR, your original choice of 7x30 Waters would be just fine.