If indeed you have the Contender and not the Encore, the 7x30 Waters is one of the best. There are some wildcats which will outperform the Waters, but not by much. Certainly not at the distances you are wanting for elk and deer.
In the Encore, my ideal cartridge for your goal would be the 280 Rem Improved with a 1-9 twist barrel.
Since you are looking at buying a new frame or SP to meet your goals (assuming you own a Contender), you have plethera of options.
Picking up a used Striker or XP and having them customized, H-S Precision's specialty handgun, MOA Maximum, and the Encore.
Personally, the break-open's are at the bottom of my list for big game hunting for one main reason: They can be extremely finicky in POI shifts with changes of pressure on the forend. Field shooting is a lot different in that you find yourself in a lot of odd positions trying to make a shot that is less than ideal compared to shooting off the bench. I want repeatability no matter what.
Sometime after the first of the year there will be a new specialty handgun coming out, rear-grip with an external detachable magazine if so desired. Since I don't have one in my hands yet, I can't say for sure what to expect, but mine will be in a 280 Imp. for what it's worth.
Can't say enough good about a tricked center-grip XP built by talented accuracy smith. I have several and they are my favorite, but they are expensive.
The MOA is a great SP. It is a rear-grip, free floated, interchangeable barrels, great adjustable trigger. I used a MOA in 7mm Rem Mag Imp to win a 1,000 yard competition that was held just outside of Sundance, WY that is specifically for SP's. Actually they had a 500 yard, 750 yard and 1K matches.
The second annual comp will be in June of 08 again just outside of Sundance, WY. Rich Mertz the owner and builder of MOA's is 307-283-3030.
There are several guys here on this forum that have or are toying with building a specialty pistol action/handgun. If any of them choose to respond that would be their choice.
Plus, there are several smith's on the forum that will customize XP's or Striker's.
Kirby (fiftydriver built my 7mm Dakota XP).
Back to your orginal question.
There are a number of cartridges that would accomplish your goals. Deciding what you want and the type of SP, type of grip (center or rear), overall weight, LER or rifle scope, etc. is where all the fun is.