Maybe we need to backtrack a little here... what exactly does the OP (@MoneyWaster ) want to do with this gun? Plink at steel? Shoot an occasional PRS type match? Shoot FTR?
Running 200s effectively really needs a dedicated chamber, and a little longer barrel, for best performance. That said, it'll still shoot pretty well as is. Same with the 155's... for years 'Palma' shooters swore that there was no way they'd make it to 1k supersonic unless pushed at least to 2950 fps, and that to do that required a 30" barrel, minimum. Both of which have been proven false, numerous times in numerous guns.
All the stuff about annealing, using mandrels, holding your nose just so... are all well and good, but to be honest, largely irrelevant to this discussion. Those things are useful if you're trying to dial in the final accuracy to where you can put more shots in the 1/2 moa X-ring on an F-class target - they aren't what's killing your hit percentage on a *2.5 moa* steel target.
I think what you really need is just practice, in the wind. The .308 Win is plenty capable, with any of the bullets mentioned in this thread - 155, 175, 185, 200, etc. - but you *have* to call the wind better than folks running more forgiving calibers, whether they be 6/6.5 or magnums. And that takes practice - lots of it.
Well said Monte. I often have wanted to try the Berger 168 Hybrid, but I cheap out for plinking steel out of my rifle. When I run out of my 175 SMK stash I'm going to use Hornaday 178 Match BTHP.