RE: Suggestions for a Left Handed Rifle
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