You're not going to get a 1/4 minute gun with your factory barrel, even if it's trued an rechambered by GAP. To get there you'll need the blueprinting AND a match grade barrel (Bartlein, Krieger, Brux, etc.). Nearly all of the "match grade" accuracy is derived from the barrel; the bedding, the blueprinting, etc. is mostly polishing the cannonball - there is some improvement, but marginal compared to the performance a hand lapped match grade barrel (properly chambered) provides. Most gunsmiths do not recommend blueprinting a rifle that shoots well unless you plan on changing out the barrel as well because the labor costs for using your POS factory barrel and a new match grade barrel are the same.
You are absolutely dreaming and completely kidding yourself if you think that you can send your factory rifle to GAP and they will return back a 1/4 MOA gun that's only a rechamber factory barrel on a blueprinted receiver. You think I'm full of it, go ahead an call them and get their opinion.
BTW, if you get a new barrel, you'll probably need to work up a new load.