That's a really odd weight suggestion in a 308win and copper. It's going to be rather slow, and something monos need is speed. With a Barnes, I'd probably not go below 2000fps impact velocity to be safe, which limits you to some rather short shots. Going by the Barne's load data, you're looking at 200 yards, tops.
Another issue, is the 180 TTSX is only marginally stable in a 1:11 twist tikka. SG of 1.17, no way in the world, I'd accept that. The BC is going to be way lower than if it was properly stable, and really significantly so. The max range is probably going to drop another 50 yards or more to maintain that 2000fps.
If you have a good 150gr load, run that. 150gr is more than enough for moose, especially in copper.