Understand I'm not talking down to anyone when I state this. I'm putting it in a simplistic academic way so that what I'm trying to say is clear.
As "bad" as a factory gun is/can be I seriously doubt that your barreled action not running true with your stock is a definitive indication that your barrel and scope are pointing in different directions. This goes double/triple for a floated barrel as the two don't interact with one another.
The scope mounts to rings. rings mount to bases. Bases mount to the receiver. The receiver is attached to the barrel. The stock is nothing more than a place for all this stuff to sit and loiter until the trigger gets pulled. Then it just transmit recoil to your shoulder.
Unless your stock is warped and contacting the barrel there's really no way for it to influence any of this. If the stock is warped then it will need to be clearanced by removing material until the barrel sits in an inert state. A scraper and a sooty oil lamp will make pretty quick work of this. Soot up the barrel, assemble the gun. Scrape the stock where the soot sticks to the stock. Repeat about a zillion times until it's right. You'll still need to do something about the other side as you'll almost surely end up with a gap, but at least the thing will point straight again.
I would encourage you to count the number of clicks from left to right on your scope. Divide that number by two. That is your scopes mechanical zero. Adjust your turrets or bezel accordingly.
Now fire a three shot group. Take notice of the difference between point of aim and point of impact.
Lets say its something crazy like 30 minutes of angle. (30" at 100 yards)
Ok, now start looking first at the rings. Is something bound up, twisted, or odd? Now look at the bases. Are they directional? Is there an offset? Now pull the bases off and see if there is a visible issue with the location of the screw holes (or registers depending on how your action is made). Are the screws reasonably straight and at the 12 clock position?
Now look long and hard at the barrel and its relationship to the receiver. Is the barrel bent? In ten years of fiddling with these things I've only seen this happen once.
If all that looks good then I'd see if I could switch scopes to verify just so that you don't miss anything. It'll give you more ammunition when you present the problem to the manufacturer or gun plumber as well.
Hope this helps.
Chad