The 120 and 150 7mm ballistic tips are two of the ones that JB says have had their jackets thickened up. If it were me, I would load one or both of those and go do some experimenting.
Or, you might be able to just stick with the 162 amax. I shot some through my 7 RM a few weeks ago. The target was a box of wet magazines. Starting velocity was 3050 fps. They didn't completely grenade at about 180 yards, and decent sized pieces of jacket still stuck to the base at 445 yards. I would probably feel confident putting one of those through the ribs of a deer, especially at distance, but maybe not a shoulder. However, your 7-08 would start them significantly slower, and rotational speed of the bullet would also be slower. Maybe try some in your own version of a bullet testing box?
My rifle loves the 162's, but, they are loaded really long so are a single-shot affair. I've seen a few nasty pics of really torn up deer with them... then again that's true of NBT's as well!
