A bolt action is usually more accurate than a semi auto because the trigger can be adjusted safely down to 2 1/2 pounds or so and still be safe...Since the stock is one piece you have a solid platform to bed the barrel into and the action is locked closed during the shot...

Forget about the 270 WSM, especially for your FL deer, the 30-06 is more than you need and I will bet your groups are getting larger because you are flinching...

Some hunters flinch all the time and all hunters flinch sometime...The fix is to match your cartridge to the game so you enjoy shooting more....

Look at lighter recoiling rifles like a .243, 7mm-08, 25-06...All of these are plenty for Southern deer...Good Luck