Depending on the game, you should be able to find a long range target load that works just as well on game.
For long range shooting, 1000yds, I'd look at bullet weights starting in the 190gr or there about. A reasonably high ballistic coefficient is nice for those long shots.
My experience shooting game has been white-tailed deer up to about 300 pounds. Nosler ballistic tips and partitions were my choice, usually in the 150 to 165 gr weight..
I used alot of IMR 4350, IMR 4831 and H4831SC.
With heavy 190gr bullets...you may want to check out even slower burning powders like H1000 and RE25
The rifle I used the most was a Ruger #1 Medium Sporter, aslo used a Rem 700 Sendero.