Unless Remington changed something on me overnight it should be 1:11.25", not that a quarter inch is worth arguing over because it isn't. 1:12 twist rates are more than fine for just about any bullet you would want to shoot in a .308. You should have no problem stabilizing the 175gr bullets in a 1:12, Marine snipers have been doing it for years, and at more modest velocities, not to the ragged edge (obviously having ammo out in the sun in 130 degree weather may have a small influence).
The advantage to say a 30-06 or 300WM with a 1:10 twist is that you should have no problem stabilizing bullets in the 210-220gr range, and shooting at larger, heavier game with them. I know of a guy offhand and maybe another that have shot 208gr A-Max successfully out of a 1:12 twist .308.
Only advantage to a 1:10 twist .308 that I could think of is that you would have a very slightly better chance of stabilizing the 178gr A-Max at a rather slow velocity.
Unless you are going to carry the rifle around the hills all day long, go with the varmint contour barrel, you don't see many pencil barrels in benchrest competitions.
A Remington 700SS 5R is a great .308 rifle off of the rack for about $1K. I had/have one and it was a very regular .5MOA shooter or better off of a bench out to a couple of hundred yards.