Re: Bullet for elk ?
150 TSX or TTSX would be my first choice in the 308. The 308 would be my SECOND choice of rifles since you mentioned the 7mag. Regardless, take both. You never know what may happen to a rifle while on a trip. I ALWAYS take 2 rifles!
Juice up the 150 TSX over the fastest powder you can find which will likely be Reloder 15 or 17. I like IMR4064 as it is my go-to powder for the 308 and since I have it on hand, I'd load up as much powder as the rifle will tolerate, then find the best seating depth for best accuracy. Even if accuracy is only so-so. Varget is another EXCELLENT choice.
You could also consider the 168 TSX/TTSX. These bullets will open readily on any elk. I'd prefer a Hornady boat tail 165 over any Sierra. Those Hornadys are not likely to roll back beyond the cannelure. Great bullets.
Other great choices would be an Aframe, AB, or Scirocco.
As for the 7mag, I like the mid range bullet wts for it and not the 175. I'd shoot a 160 class bullet with H1000, Retumbo, Ramshot Magnum, VV N165 or 4831 or 7828. H1000 and Retumbo would be my top choices.
If you are wanting great velocity and not too concerned about temp variations, definitely look at Reloder 22. I LOVE this powder.