For the price of a TRG you can have a custom 338 built, so that is the route I would go.
Look a the Snake 2 in the gun photo section. Just built one. Snake 2- 338 Lapua Ack Imp
If you are going to go the big case route then 338/408 route is the way to go. Bruce Baer has his Big Baer and Kirby Allen has his 338 AM.
If you want a 338 on the 404 case then Mark King at Mark King Custom Rifles in PA builds them and has reamer and dies. He might build on the 338-416 also, but I would go with the 408 first and then the 404 (RWS brass is why). Look at Joel Russo's 3.8 inch group at one mile shot with a Big Baer here on this site.
IMO custom action is the way to go instead of taking an off the shelf and working it over. Normally costs less and will be worth more.