I'm shooting a 20" Reminton LTR with a 6 groove 1-12 and it stablizez the 208 Hornady just fine. I'm shooting at 7000 ft elevation and the elevation will make a difference. I think Berger has a stability calculator that might help you.
I have that gun and I shoot 175's all day long. 168's do just as well. Mine is in 308 too, so I had no interest in shooting heavier than 175 because I like to balance velocity too.