BGH,
I fully agree with the suggestion to try other brands and types of ammo, your gun might not like Swifts. As far as your rifle is concerned the Sako 75's are known for their accuracy, as are all the .375H&H's I've ever tried. My old Browning Safari shoots Barnes X's into 1 1/8 and everything else under an inch. In fact Hornady 300gr RN crowd a 1/2". One suggestion is to rest the back of your hand on the frt bag and hold on to the forend, because the forend bouncing off the bag can mess up the grouping. It can also affect your zero between what you shoot from the bench and what you shoot from a field stance.
I don't have any idea what Factory loads to try as I only shoot reloads. I have heard good reports about the Hornady Heavy Mag loads, and the Federal prem stuff.
The guns likely fine it's just looking for the right diet is all.