Been there, done that. I was basically pissing in the wind every time I tried to shoot past about 700yds at sea level.
In the right conditions, especially at altitude, the .308 can stretch its legs nicely with the right load.
The new Tipped Match Kings, Bergers, and bullets like that are great.
New Tipped SMK's
The 155gr TMK has a listed G1 BC of .519, which is awesome really.
The 168gr TMK is .535 G1.
That brings the .308 back into 1000yd territory.
Use a fire control group that has a low mass hammer and full power hammer spring, a heavy high end barrel, and use quality components plus good load procedures, and you're on your way.
If you stick with the 155gr and 168gr, you'll be fine with a RLGS and 22"-24" barrel. You could go extended length gas system and focus on 175gr, like the new 175gr TMK with .545 BC and run the slower burning powders. You don't see huge velocity gains going from 22" to 26", as the curve flattens out there.
Go to
Velocity Estimator to run some comparisons with loads, charge weights, and barrel lengths.
If you are looking for supersonic out to 1200yds, the newer high BC target pills for .308 are your only real ticket, combined with barrel length.