Building one would be the way to go. You can get the Howa action through some dealers for less than $377, so figure the $350 range, plus about the same for a good tube, and your Axiom stock at $250. That's $950 with a decent adjustable trigger already. A good bedding job, rings, and bases puts you around $1100 give or take. Not bad for a precision rifle.
I'm not going to start a debate over the .308 vs. .30-06. My point was if you were looking for a rifle that you would rebarrel to .30-06 and said rifle was ALREADY a .308, there wouldn't be a lot to gain by going to the '06. In a custom rifle build you have the option of having anything you want. However, you clarified that you were originally talking about the build and not the swap, which would be the way to go. I think you would be pleased with the Howa/Axiom combo if you decide to go that way. These are great rifles
t2e