Shawn is right on the money. If you want to use the Rem 700 receiver, the 338 Edge is about as much as you can get into a Rem 700 comfortably.
That said, with significant modifications, you can chamber the Lapua based rounds in a Rem 700 but it costs more and in fact, you could get into some custom receivers that would serve you much better without alot more $$ compared to a Converted Rem 700.
The 338 Edge is an easy fit into the Rem 700, especially with a Wyatts extended mag box.
As far as the 338 AM, again, Shawn is right on the money, its a no go. Only receiver I really recommend at this time is a BAT Model M receiver for my 338 AM. I am not saying there are not other quality receivers out there that will work but for quality, stock inletting choices and strength, this is my preferred receiver for my 338 Allen Magnum.
Allen Precision Shooting
Home of the Allen Magnum, Allen Xpress and Allen Tactical Wildcats and the Painkiller Muzzle brakes.
Farther, Faster and Flatter then ever before.
Web Page: www.apsrifles.com