Excellent input thus far. Like the heavy barrelled field piece guns, as much for the conventional reasons to have a heavy barrel, but also a gun that is muzzle heavy does settle better on target. My Sendero was the first issue, and not nearly as pretty as RJ's.
Glass is important, as mentioned. Out to 800 you'll have to dope, so clearness, consistancy, but also ease of adjustment is important.
I personally like the idea of a heavy 30 for this task, although 800 yards is just doable with the 308s if properly fixated. The reason a larger 30 catches my eye is that its capable of handling heavier bullets, which are easier to dope and less prone to give you any wobble way, way out there. You'll need to match your bullet weight to the twist, of course, but I'd start heavier than 168 and work upwards from there. Sierra offers bullets as heavy as 240 grains, although I think rifles twisted for it are not factory propisitions.
One advantage of the 308 is that it has been there and done that, and there are reams of data to compare it against. The 300 WM is catching up, the military started using these for the reasons articulated above, and they are building useful references in quantity. That said, don't get frustrated, your rig and loads will have to matched by practice, and his is a time consuming process. I've owned my Sendero for 16 years, (7RM) and I'm still working this out. It is a fine and plesant misery.
My best to you Sir.