The one guy who ever got good results at 1K with 168gr BTHP's in a 308 Win was using a 1:13 twist in his barrel, which goes against the common wisdom about twist rates and transonic bullet transitions.
I've got sub MOA at 1000 with Sierra 168 HPMK's from a 1:13 twist. They left at about 2770 fps from the 32 inch barrel with 44.5 grains of IMR4064.
It's not the the rifling twist alone that stabilized bullets in flight for long ranges. It's the rpm's they start with. Slower twists and high velocity spins a given bullet the same rate as a fast twist and low velocity. That 168 needs to be spun at least 150,000 rpm out the muzzle to stabilize it to 1000 yards. And leave at least 2700 fps to remain supersonic through 1000.
2600 fps, 1:12 twist = 156,000 rpm (M852 match ammo from M14, M1A; subsonic at 1000)
2770 fps, 1:13 twist = 153,415 rpm (supersonic at 1000)
Note that Sierra 168 International Match BTHP (later renamed a Match King) bullet was first made for free rifles used in 300 metre international competition. They were shot with reduced loads giving about 2500 fps out of the 1:12 twist 26 inch barrels used. Excellent gold medal winning accuracy was attained in the Olympics.