The above post is good advice and your best option. The others that come to mind are not nearly as practical. You can by rounds with 'premium' bullets designed for penetration...but they cost more. You could make handloads for your 300 with said bullets and reduced velocities...or you could only take long shots at game.

I don't suggest any of them, but they are options. Like Fornra said, you going to ruin some meat with a 300 so just be picky about which meat you ruin.