Pharo,
I hunt some country that looks just like that,I have .450 marlin thats is suited perfectly for it.Then again 200 yds is a strech for,start getting in to the rainbow factor.
Taking the BLR's out of the equations,you lose the flat shooting magnums,so you are down to winchesters and marlins.
Now if you go with a bolt action,the 350 Rem mag come to mind,lots of power out to 300 yds,yet still flat enough shooting.
Now it is not very "main stream" so ammo is not that avalible.

So here is what I would do,I would find myself a good used .338 win mag.
take it to a gun smith cut the barrel down to 22",put a straight power 4x scope,cram that thing full of 225 gr slugs and WALLA problem solved.
One heck of a carbine.Probaly get the hole thing done for around 600 bucks.