The Nosler Loading Guide list a load of RL 15 at 39 grains for a 160 grain bullet at 2,593 fps.

Nosler I have found is pretty right on the numbers for
saami max that they list.

I am going off memory but I believe the 708 is at 62,000 psi rating. That being so you could add a grain of powder bring it up to 65K to add another 40 to 50 feet per second.

Add to the fact a slick moly bulet, then add another grain or so of powder and your right at the max for bullet seating into the powder (which btw I've found Remington boxes maxing at 2.830 COAL and no more) and it reaching right at 2,700 fps.

So yeah, it's probably doable.

My guesstimator says Tryme is loading 41 to 41.5 grains of RL 15 to
get at 2,700 fps. His pressure is probably in the ball park of
65k to 67K. The ogive of the Amax works for him being more nose than body contact to the lands.

That said,

I would never use it out outside of Sitka and Coues deer.

I would rather use the 308 for elk, bear, and large mule deer.