Wrong Way,
I've used a 350 Mag on Moose and Elk a fair bit. Although I've never had a bang flop (except on deer), I've never had to follow either critter more than a few steps from where it was hit to find it piled up.
A lot of junk has been written about the 350, some of which is regurgitated in one post above. The 350 has just a slight bit more powder capacity than the Whelen, so it will beat it by a small margin in direct comparison. The trouble with the whole Whelen/350 thing began when the boys started looking at loading manuals. The Whelen data was usually on a 22 or 24 inch BBL, while the 350 was usually on an 18 1/2. If you've got any old manuals, check it out.
As you likely know, the 338 requires a long action and .............
You can discount the stuff (which always comes up in a short mag discussion) about the short 2.8" Remington mag box limiting the 350 by restricting COAL. To seat a 250 gr to 2.8" restricts the 350 by about 4% of it's total powder capacity, which keep in mind is already a bit above the Whelen to begin with. Since there is roughly a one to four ratio of powder increase to velocity gain, restricting the powder by 4% equals a 1% loss of velocity. With a 250 gr going at 2600 fps, that boils down to 26 fps. So, definitely build on a short action, as you originally mentioned, if you go 350.
If you're building custom, I would recommend you consider 1-14 or 1-12 twist. The factory Remingtons were built on a 1-16 twist, which tops out at about a 250 gr spitzer. There are a few good bullets made heavier than 250 and it would be nice to be able to try them in your rifle.
The 350 mag works wonderfully with 250 gr bullets, of which there are several good choices. If your shots are going to be under 200 yds, I'd use the Hornady 250 Round Nose. Always accurate, shorter slug helps seating depth and stabilizes better, and it mushrooms perfectly at 2600 fps muzzle velocity. If you want something more aerodynamic, the 250 gr Speer Spitzer is a great bullet also. I use both. My preference is the Hornady RN, as the Speer seems just a bit too hard for proper mushroom at 2600 fps, based on the animals I've shot so far. If you like premium bullets, the Nosler Partition in 225 or 250 and especially the Barnes Triple Shock in 225 should be considered. If you want a 200 gr load for deer and what not, the Remington bulk 200 gr PSP is quite hard and shoots well.
For powder, so far I like IMR 4320 and Win 748. Lots of folks who know like R15 in the 350.
For my money, I'd build on a stainless M 700 (more aftermarket choices, one more scope base screw hole), 20 or 21 inch barrel 1-14 twist, fibreglass stock at a total weight of 6 to 7 pounds, depending on your recoil preferences.
