Backwoods,
I lived and hunted deer in West Tennessee for 30 years. I know that you are right when you say your shot could be anywhere from 40 yards (woods) to 300 yards (beanfield).
Let me give you a big time piece of advice, though. When I first started hunting, I had a 7mm Rem Mag. I thought it would be a great deer rifle. WRONG.
On two occasions, I shot large deer at close range in the woods, broadside shots, and the bullets just zipped right through their bodies, with no expansion whatsoever. It was terrible. I had to shoot one deer 5 times! before it went down for good, and another 4 times. I didn't lose either deer, but I almost gave up deer hunting over this. They kept getting back up on their feet and trying to run away. I might as well been shooting full metal jacket bullets. Tiny holes in, and tiny holes out.
Your 300 Mag (like the 7 Mag) was not designed for close range deer hunting. It was specifically designed for long range shooting of relatively large tough game.
If you are going to hunt where shots are 100 yards or less, then please take a .30-30 or a .35 Remington instead. It will put them down very quickly.
If you are going to shoot over a 100 yards, then maybe you can use the .300 Mag, but you will need to use light, softnose bullets, no larger than 150 grain. Downloading it to .30-06 power would help too.
Hope this advice helps you out. I'm just trying to save you from making the same mistake that I did.
Best, Mannyrock