You might want to provide the muzzle diameter of the 30/06 barrel, as that will be the limiting factor of how large a calibre you can bore it out to. You need a barrel wall thickness of around .125, so subtract 0.25 from your muzzle diameter to give you an idea of what the largest diameter you might be able to have it bored out to.

From a practical perspective I dont think you will find anyone interested in re-boring barrels in Oz. Sprinter in SA used to re-bore barrels and you would need to check whether they still do. I had a light profile 30/06 barrel bored out to 338 many years ago and accuracy was so so. The best it would do was around 2" at 100 yards.

Personally, I think you would be better off selling the barrel and buying another factory barrel if you think you need another.