I would not expect Silver Bear or Prvi to be particularly accurate ammo. As jim580 said, try some domestic ammo from the Big 3, and go from there. Rem CoreLokts have a well-deserved reputation for accurate, plain vanilla hunting bullets. You could always try some match ammo and see what the rifle can really do.
BTW, whomever told you "heavier is better" got it backwards: typical .30 rifle twist is 1:10, so your Howa's 1:12 is relatively slow twist. Heavy bullets are generally longer, and longer bullets require a faster twist. Google "Greenhill formula" for the details of twist rate and bullet length.
That said, the 1:12 should stabilise a typical 150 gr spitzer, which is about optimal for the .308 Win, anyway. It might be dodgy with a 180 gr bullet, and all bets are off for the 200 grainers.