I'm not trying to rag but it sounds like you're trying to fit a square peg in a round hole with this one. The .338 EDGE was designed to be a long range round throwing big pills out of long barrels. It kind of negates the purpose out of a shorter barrel and it's almost a waste.
I think the first question I would have would be what do you want to hunt with it and at what range? Depending on that you may be more suited to building a climbing rifle in something traditional like a .270, .280 or .30-06. There's plenty of wildcat options for those too if you want something that's a little different.
Now that the practical stuff is out of the way, it would be pretty sweet to feel the blast from that thumper!