Its possible to use a regular 700 action but only with a number of mods. You have to open up the bolt face to handle the .585 rim diameter and it won't leave much of a ring on the bolt face. You will have to mod the magwell/receiver unless you plan on seating bullets deep. More likely you'll need to ignore the mag and single shot. If you do want to use the mag you also need to mod feedlips and the follower. I wouldn't fool with a regular 700 action to build one, I'd go with one of the custom actions like the defiance that is already set up for .338 LM. It may cost a bit more in parts but it will save a lot of time and effort and you'll get a better rifle in the end.
Frank