IMR 8208 is an excellent choice for bullets in the [approximate] 155 gr to 175 gr range. I personally think it's a tick too fast for 180+ bullets, but it will certainly work even with the slightly heavier bullets. As has been mentioned, H4895, Varget, or IMR 4064 would also be good choices, but there are many more, depending on what you can find with regard to availability. Below I attached a burn rate chart with the most commonly-used powders for .308 Win boxed in green. Obviously, powders at the upper end are faster burning than those at the bottom. FWIW - Varget and H4895 are available, but you have to search diligently and buy some immediately when a store or online vendor receives a shipment; they don't stay around very long.
You did not mention whether you intend to load to mag length or single feed. One bullet in the weight range you listed that might be worth looking into is the Berger 168 gr Hybrid. It has a very good BC for the weight, and does not suffer from any boattail angle-induced dynamic instability issues like the 168 Matchking. I have had very good results running the 168 Hybrid over H4895. I'd imagine 8208 XBR would work equally well with it. Another choice might be Berger's 175 gr OTM Tactical bullet, which has a tangent ogive and is not too finicky with regard to seating depth.