To be honest, the good old 25-06 is a stone cold killing machine out to right about 550m or so, and it is pretty reasonable on recoil. You have to reload to get that kind of performance I believe. The Berger 115 bullets and H1000 or H4831SC, or IMR7828SSC are really nice.
That being said, if you can tolerate the recoil of the 300wm then it will hammer out to right around 1k or so... for a certain series of "Prices"
The 7mm RM of course is also great..
The 30-06 "is never a mistake" according to the immortal Townsend Wheelen.
The 6.5's are really nice, and I am very much a fan of them. The .260, 6.5 Creedmore, and the 6.5x47 Lapua are all very nice, and would likely do what you need.
While I love the .308, for me it more or less runs out of steam around 450m or so for conservative shots on animals. I do not enjoy tracking wounded animals for hours on end.
Decisions and Choices!