I would get a Ruger M77 mark 2 in a 300 win. mag. with a very good scope, I use Nikon Monarchy 3-9 but would go with more scope power to shoot longer distances. I shoot a 3 round in a quarter size hole at 50 yds. with nosler tip 180gr. bullets. I have never had a deer complete a full step when being hit with this load and gun, shot placement is very important. Never take a iffy shot, the animal deserves a clean and quick kill if possible.
The OP already has a .270 and a 30.06 so no need to buy a 300 mag unless he just wants to add to the rifle collection. The 300 also kills at both ends.