Can one have his 308 reored to 338 and then recahambered? Compared to the cost of a barrel what could one expect to spend?

I am ususally on the opposite side of the fence on this subject, as I like the idea of reboring.
I have found the prices to be around $4-450 for what you want to do. A new quality barrel, fitted, chambered, blued, reprofiled if you have a "nonstandard" barrel channel, and if you have open sights, seems to run quite a bit more, probably around $600. Again, these are just rough estimates, but that is what I have found in my research.
Remember also, if you get a new barrel, you may or may not be able to match the bluing on your receiver, meaning you might end up with a "two tone" firearm.

There are certain limitations to reboring. The barrel has to have enough metal in it to allow for .100" wall thickness after the rebore (some require .125"), so your .308 barrel will have to be at least .538" at the muzzle. Moreover, there should be no deep screw holes for front or rear sights which would create a wall thickness problem.

I would suggest you consult Delta Gun Shop/Clearwater Reboring (www.deltagunshop.com). They have done several jobs for me and are in the process of another. They have a price list which is pretty self explanatory.

Thank you for the info. I will check Clearwater Reboring. Yea I would like the whole gun to match. The two tone had me thinking about reboring instead of rebarreling.

You might also check with Dan Pedersen at Classic Barrel and Gunworks.
www.cutrifle.com

You will be a lot happier if the original barrel is cut-rifled.

Check out JES reboring. $250 and IIRC, he does .338" now