"They are generally considered a 1/4 MOA barrel, a good hunting or varminting barrel, not a benchrest or match barrel. In order to shrink that group by 50%, you have to spend 3-4 times as much on a barrel. In order to shrink it by 75%, you have to spend 6-7X as much."
Wait, wait, wait; 1/16 MOA?! Does powder even burn consistently enough to realize that? How are you arriving at that number? I thought the fixture-mounted 'rail guns' operated with remote triggers only get like 1/4MOA, using every impractical trick there is.
One thing to note with GM barrels, is they are button rifled. In turning several, I have found that some warpage & chatter seems to occur in diameters under 5/8". Not something a 1/6MOA benchrest shooter would be interested in, but the distorted metal --even normalized/stress relieved afterward-- might make turning the profile very narrow a bit more difficult. I've not had the pleasure to mess with cut rifled or hammer-forged blanks, as they are $$$$, so I can't say if they'd suffer similar issues.
Regardless of barrel, the chamber, crown, and bolt engagement will have infinitely more impact on accuracy (as will selection of bullet/load for the twist rate).
TCB