My favorite rifles are the 6.55x55 Swedish Mauser, 338 Win Mag & the 06.
The 06 with 165Gr. spitzers will do a fine job on your hunt and shoot somewhat flatter as well.
And as someone else pointed out GET used to shooting 300 yds.
I always use a bipod and shoot from the prone position as much as possible, this allows me to drive it home out to 400yds+.
If you are hunting from horses you can always put your bipod on afterr you dismount and remove your rifle fom the scabbard.
Good luck