For cleaning out Hog populations, I would go with the 6.5 PRC.
Light recoil and decent ballistics.
This is assuming the gun shoots well enough to kill at that distance (760 yards).
How does it group at 800 yards in good conditions?
If you are going to be shooting off of at that portable shooting rest in the picture, how good can you group with it at 700-800 yards in good conditions?
Factory ammo or reloading?
What bullet are you considering?
If it shoots well in your rifle, the 147 ELD-M would be a consideration
Great post XP. I'd also throw this out there, how often does the OP practice at those distances? If possible, I'd set up steel plates in those open spots, and practice. He will find out real quick, which rifle works the best for him. I also like the 147 ELDM.