My vote is anything in .284 bore. If you're only going to own one centerfire bolt rifle, the .280 is my choice. If you're a multigunguy like I am, the 7mm-08 and 7mm Rem Mag come into play.
I looked at the ballistics of the 7-08 and it looks flatter than a 308 so that does look good. I know they make 7-08 ARs but I'm not sure how reliable they are compared to 5.56 ARs, which I have a couple of.
But if I'm looking for an all around hunting SHTF rifle something tells me they would be hard to beat.
I have an AR10 pattern rifle in 243, and while I like it a little it doesn't see much use. Partly because it is heavy and less handy than a similarly chambered bolt rifle is capable of being, and partly because AR10 magazine constraints hold it back from using 105 AMax to their potential. Matters would be worse in 7-08, with a 162 AMax.
Either configuration would handle shorter bullets well, like TSXs. But you still don't get away from the weight and ergos.
For an 'all around' hunting rifle I wouldn't go with any AR config. For something dedicated to a run and gun scenario in a target rich environment I can see the application. I plan to give that a go around some hogs, maybe even hogs from some kind of conveyance.
I wouldn't be able to advise RE: SHTF. My reality is far too interesting to dabble with fantasy.
I love my Browning 7mm. I don't think you can go wrong with a 7mm for a multi game gun. I have never fired factory loads. I worked up some hand loads and have been able to get some terrific groups. 7mm is also available in several different bullet styles and weights.
A good bolt gun in .270, if money's tight look at Steven 200. Then find a used 336 in 30/30 cheap/available ammo, light and handy. These 2 should cover you for anything in KY....Good Luck..........Duce<><