I had a GAP Crusader in .308 that shot the 208's with incredible accuracy. Most I ever shot was 529 yards and it was about 1 1/2" group. Only had a 22" bbl with a 1:11.25 twist.
I now have a custom 28" bbl 1:11.25 that shoots the 208's just fine also. Is slinging them at 2650 fps. And shoots 1/3 moa most of the time. You'll most likely be fine.
I have 2 win mags. One is a Rem 700 5R MILSPEC w/ a 26" bbl. it LOVES the 208 amax over 76 to 77 grains of H1000, and 72.5 grains of Reloader 22. Also found a really good load ( extremely FAST) with PP4000mr. 72.4 grains has me at 3,000 fps from a 26" bbl!! RP brass and fgm215 primers. Kind of a hotter load though.
74 degrees w/ oheler 35p at 20 ft.
77.0 H1000- 2900 fps
72.5 R22- 2920 fps
72.4 Pp4000- 3,000
Most accurate load was the h1000 that day. But last summer I shot some groups at 500 with the 4000 mr load that were unbelievable.
You may want to also try the 200 Berger.
My load for it is 78.0 h1000 , Nosler brass, fgm215. It shoots 1/3 moa at 100. I'm guessing its in the upper 2900's. 2980 to 2990 fps.