Anachronism,
A properly set up Rem 700 will certainly handle the strains imposed by the 338 Lapua magnum but you will need to use a special feeding system for the fatter case. The H-S Precision DM system is what I would recommend.
Ecomonically??? That depends on your definition of the word. The H-S Precision will set you back around $200. The bolt face will need to be opened up and a sako style extractor fitted. May need some feed rail mods to fit the DM system.
I will be testing this platform here soon and see how it performs.
I will say that I would only recommend using Chrome Moly receivers for such a conversion because the steel is harder then stainless and will resist bolt lug and bolt lug recess set back better then the stainless receiver.
Just a bit of extra insurance if oyu will.
With the release of the 338 RUM, this conversion is really not worth it though. Sure brass quality is much better for the Lapua but actual ballistic performance is pretty much identical with top hand loads in the 338 RUM.
TO convert your 338 WM to the RUM you would simply need a new RUM mag box and you may need to open the feed rails on the receiver up slightly.
Some I have built using the standard belted mag receivers needed the feed rails opened slightly some did not. This is a very simple process though for a quality smith.
Price wise it would be vastly easier to convert to 338 RUM and ballistic performance would be for all intent and purpose, identical in the field.
IT is also a much better fit in the Rem 700 receiver obviously!!!
Good SHooting!!
Kirby Allen(50)