Been there, done that. IMHO there is no practical way to make a repeater 338 Edge on a Savage long action.
I ended up buying a Stiller Predator and using the 4" Wyatts box. Even then, the modifications required to the action were considerable. A decent amount of material has to be removed at the rear of the mag box opening. I did this with a Dremel of all things and it came out fine. But it took a long time. The bolt stop also needs to be modified to allow the bolt to come further back to pick up the rear of the long cartridge.
I used a McGowan Remage barrel with their nut. The gun is crazy accurate. I took 3rd in a 2000 yard competition against much pricier custom guns and took an elk at 700 yards last weekend with it. Given the wind I elected to use a sighter. I slipped under recoil on the first shot and didn't spot it, so I had to use the second as the spotter, and dropped the elk with the third. So having a repeater to do all of this in under 30 seconds was a big advantage.
I can't speak to your weight goal. Mine has a steel Sendero contour barrel 30" and McMillan A3 Sporter magnum fill stock and Heathen brake and comes in at 14lbs scoped. I don't know how much weight a carbon barrel would drop but an 11lb 338 Edge sounds pretty aggressive. I did pack mine 8 miles back into rough country to take my elk.
