I've had a couple .338 Edges, still have 1, a Defensive Edge Canyon Rifle. An Edge doesn't get much "Edgier" than that. (Thanks Hotshot

) Mine's built on a Bat action with a 30" Hart. The big Bat action and long mag box eliminate the downsides of the Edge.
The concept of a "poormans Lapua" made more sense when there wasn't a .338 Ultra. As it stands, If I were starting with a Remington action today I would just go with the .338 Ultramag instead. You would have a fighting chance of useing your magazine, and the increase in case capacity isn't worth mentioning. If you do much for mods to the 700 action it can end up costing as much as a custom action. If you're going the custom route you may as well go with the Lapua and get the good brass.
I initially thought that going with the Edge chambering opened up one source of premium brass, that being the Nosler but that proved to be a disappointment. If you are stuck with Remington, you may as well use the Ultramag. Then there's the necking up. It is a simple run over a tapered expander ball but mine come out horrendously crooked. Sure they staighten right out on the first fireing, but the cost of fireforming negates any price advantage over the Lapua. I've got Sinclair expander mandrels comeing that may minimize the initial run-out error, but I can't help thinking that necking up a case and produceing an instant doughnut is the hard way to do things while not saveing anything.
Whatever you chose to do, throwing 300 grain bullets way out there is about as much fun as you stand.