I would start with H-4350 myself.
At those distances, it will do a great job on all of animals mentioned. You will have performance similar to what a 308 Winchester does in a rifle.
I don't have a problem with a 130 grain tripleshock for elk.
The main thing with the TSX is if your barrel likes them or not.
If not, the Accubond or Partition (heavier weight) would work great too.
It has been snowing most of the day here.
Using your pack as a rest will get you nice and steady for those distances. If you do all of your shooting from field positions once you get your load developed, you will have no problems.
What kind of optic are you considering?