I would take your time and make small changes first like change the stock and bed it then see how it shoots, since you already have the gun.
then play around with some bullets/seating depths if you reload and see how much freebore you have. for 300yd shots you probably don't need a super low drag bullet, so you have some options to play with to see if you can get a particular bullet to shoot better.
a 7mm mag will have less barrel life than say a 30-06, so after tinkering, bedding, working on some bullets etc you will have 500rds through the barrel (hopefully) and be about 1/3rd of the way through the barrel life.
i'd recommend a barrel replacement vs setting the barrel back. if you want to chamber it yourself you can get a prefit short chambered barrel, or you can go with a remage system from northwest shooters supply and use a barrel nut. I shot with a guy back in December and he was using a custom action (bighorn TL3) with a criterion (NSS savage prefit) in 6mm creedmore and he was hitting 1moa steel at 600yds.
a stainless steel remage barrel is about $300-$350 depending on length
http://northlandshooterssupply.com/barrels/criterion-remington-remage/
from what little I know about the subject, most factory actions are or should be capable of 1moa accuracy, the weak points are the stock, barrel and shooter interface. the barrel could have a few problems: the chamber or crown could be cut poorly, the rifling could be imperfect, the freebore could be excessive or the barrel itself could have stress in the steel and it could flex as it heats up.
the shooter interface is one that may get overlooked, does the stock fit you? can you get behind the rifle in a repeatable manner? is the trigger crisp and repeatable? can you pull the trigger in a consistent manner that does not disturb the sights? are you flinching? (shoot with a buddy, walk away from the shooting area, have a friend load the gun and close the bolt and you take single shots, have your friend randomly NOT load the gun, but where you are unaware. you will quickly identify event he slightest flinch. the same could be done alone with dummy rounds, load them the same way and mix them in with live ammo so you are blind to the process)
you claim you are a 1/2 moa shooter off of a tree, while I agree with
@Varminterror i'd love to see you demonstrate that, I will also assume you are not a limiting factor in the rifle's accuracy. off my belly I am a 1.5 to 2 moa shooter with my $4,000 custom rifle with all the bells and whistles, on my belly i am a consistent 5/8 moa shooter and I am the limiting factor