I and two friends hunted in Valdosta, GA, back in '84. My one buddy used a Remington 742 that would only shoot the Remington 180RN factory load well, but it was well indeed! He shot a spike around 80yds, a big bodied deer weighing around 160#. Shot tight behind the shoulder, it made a big mess inside, and about a 50 cent piece exit hole, no bloodshot meat, impressive.
On another lease, in Texas, another friend used a 742 and the Remington factory 220RN, he hunted in the woods, all close shots, same results, dead deer, no bloodshot meat. I used my dad's 742 30.06 with 150 PSP corlokt factory, dead deer, lots of bloodshot, ha. That particular rifle was a jammomatic, but I never shot anything twice with it either. It did better on meat with the Sierra 165BT in the then new Federal loading. Deer don't need a lot of killing, but no use tearing them up either. Of course, I used fast bullets in lots of calibers, but I made heart/lung shots and didn't ruin a lot of edible meat, although if I got too close to the shoulder, it was ruined. At the ranges you hunt, a good 180RN around 2500-2700 is super. go for it!