When it comes to LR hunting the TC's are not my weapon of choice.
I like the XP-100's,
MOA Corporation Homepage
MOA Maximum Handgun
The Striker's are typically quite accurate but have a unsatisfactory trigger.
If, converted to a rear-grip, you can get a good trigger.
Purchasing a non-designated action Savage Target action or almost any action you can think of, and then you can build a rear grip SP.
Cartridges I use the most would be: 6.5-284, 6.5 WSM, 284 Win, 7mm SAUM or WSM.
The 260 Rem and 7-08 Would also get you there as well, but would be pushing it to the edge of their capability in a SP
I also have some larger cartridges that would be overdoing it for 5-6 hundred yard hunting.
A break-open that I really like but have not had the time to use a lot yet is Freedom Arm's Single-Shot specialty handgun.
Interchangeable barrels and the barrel is free floated.
The chambering I will be using the most is is a 6.5x55 Swede Improved
The MOA SP also has a free-floated barrel.
This would also get you to your desired max distance on deer.