Tikka has come back with a left handed offering in a T3(late fall). I believe .308 win was one of the chamberings they were offering as well.

I am a southpaw my preference is LH Rem 700's. I also own a LH Browning SS Stalker.

Like mentioned Savage and Ruger offer a number LH rifles.

I think you'll find most manufacturers that produce LH models will have a .308win offering for you to consider.

Good luck