Great idea! However, J.D. Jones did substantiall what you're contemplating with his .411 JDJ, a .444 Marlin necked down to .411. In a hand gun (Thompson Center Contender) he gets about 1700-1800 with a 300 and 400 grain bullets. You should get about the same, maybe better considering the longer barrel of the carbine. If you compare the .308 and the .444 marlin shell casings, you will notice that they're substantially identical except that the .444 is rimmed and is a little longer than the .308, but the diameters are the same. Hence, .411 JDJ loading data would be a good starting point for your .411-356. Performance in the .411 JDJ should be substantially similar to what you would achieve with your .411-356.
The only problem is that most bullets are round noses or spitzers and not necessarily suitable for use in your rifle's tubular magazine. I'm sure there are some flat point cast bullets that would be suitable though.
I had a similar idea to do this with the .308 win case. Neck it up to .411 with an Ackley shoulder. This was done with the 30-06 case and it's called the .400 Brown-Whelen. I think they get about 2.500 fps with a 300 grain bullet and 2200 fps with a 400 grain bullet. I thought it would be cool to do on the 308 case, just using the 400 Brown Whelen and stopping short of the 30-06 length. I was set to do it with one of my mil surp mausers. Something different to do with the thousands of .308 brass I have laying around. I was really turned on about it, but got interested in something else. (Blonde hair, long legs, short dress). The .400 Brown Whelen was written up in Wolfe Publications "Big Bore Rifles and Cartridges" if you have a yen to read it.
I thought the .411-308 would be kind of cool. It would duplicate the .411 JDJ which has been throughly proven on big game by J.D. Jones and others. Also, you could use .41 cal pistol bullets and cast bullet loads. As I get older I really like big bore rounds. There is a different dynamic to shooting those lumbering, big bore heavy bullets and seeing the big round holes they make in things.
Keep us posted on how you make out with this idea.