I don't think much could survive a 180gr Nosler Accubond or Partition. In a .308 I would work a load up using RL-15 or Varget. The 165 sierra gameking would probably do the job also.
Awesome! RP cases, Fed210M, 180BT/AB, 43 grains RL-15 to fit in the magazine. This shoots very well in my Smith MP10.
If it is more deer than elk, I would lean more towards a 165gr. 44gr Varget under a 168gr NBT does well for me. This bullet is pretty tough, especially at your 16" 308 velocities. I have taken a handful of good sized hogs in my 20" with it and never recovered one.
All the component issues got me digging and one of the better loads has been 46.5gr of Hodgdon's CFE223, driving a Nosler 165gr AB. These are loaded into LC cases, and fired by Tula LR primers. Good velocity, not by chronograph, but by drop at 300M. Commercial cases may handle a bit more powder. Barnes TSX would be good choices also as long as powder space doesn't get to be an issue, magazine limits can dictate loads.. The 165gr is a good compromise of weight and velocity, and most shoot well in my FAR308.
I would NOT use the sierra game king 165 after having loaded it for a number of years in 06 for a buddy, had that bullet both not expanding and coming totally apart.
And performing normally.
I don't shoot an AR but my go to bullet in 308 since I had a bolt gun rebarreled has been 185 bergers. Same bullet we shot for years in M14s..
This is late but I think informative.
I would steer towards a faster burning powder since your barrel is only 16 inches. No reason to create a big fire ball outside your short barrel with a slow burning powder.