If you really want .338-'06, your only trading option for a factory rifle would be Weatherby, as I couldn't find anyone else (quick search) making that caliber.
Do you want to keep that rifle? If so, you have two choices, the first being to rebarrel. The cost will depend on what barrel you want, material (SS or carbon steel), and who does the work. Others might have more exact figure, but the job will run at least $200, with $300 or more for a good quality barrel and good work. A top quality or stainless steel will run more.
The other alternative is to have the barrel rebored and rerifled, but the drawback is that not many places do that work and most are backlogged to at least the end of the century, but maybe someone will know of a place that can do the work within a reasonable time.
Jim