Scooby,
Brownells used to send a list with their catalogs to dealers of suggested service prices. Back in the early 90's it was $40 to rechamber. Today it's probably $60-$80, but that's just labor. If Reamer rental is involved you'll have to add that.
You still have the issue of whether or not there is enough metal. If you have something beefy like a Shilen #7 contour barrel to start, you'll be fine because the thick portion goes forward of the receiver 4". But if you start with a light sporter one, like a #3, where the thick portion is only 2.5" long, you may not. That will have to be determined by the gunsmith. But I would think that in most instances there will be enough to go from .308 to .30-06 AI because you don't need to set the shoulder back or re-thread the barrel. If you went to regular .30-06, the added labor is unlikely to make it as worthwhile.
If you load the .30-06 and the .308 to their respective SAAMI maximums (60 kpsi vs 62 kpsi), you get about 100–150 fps more velocity out of the .30-06 from a 26" tube, depending on the bullet weight. Add another 50 fps for the AI format, and you should have a 200 fps advantage over the .308. It's not magnum but it's not nothing, either.
With commercial loads you often don't see that .308 and.30-06 difference because the latter is more likely to be underloaded out of liability concerns for old rifles. The velocities were much closer when both were constrained to using 4895, which the .308 handles more efficiently. But the '06 can actually handle a slower powder better than the .308, and that picks up its potential. You just can't count on using a slower powder in the Garand or other gas guns as readily.
Loading for yourself, you can work up reasonably to maximum performance for your weapon. If you work up based on brass pressure signs, you'll likely discover your gun is happy running .30-06 AI at the same pressure as .308, in which case another 25 fps will be picked up.