Is it legal to 'masterkey' a shotgun to a rifle?

[MuzzleFlash]

Greetings! I'm a frequent visitor here but it's my first time signing up and posting. The forum's informative enough that I haven't had to ask anything before.

I've got an Ithaca 37 and an AK-47. I'm amazed how well the shotgun lines up under the AK. It looks like it would be a simple, though somewhat pricey, task to have a fore grip custom made for the AK that would drop down and secure the shotgun in place.
So here's my question. Would a stockless or pistol grip 16"+ (EDIT: 18"+? whatever the shortest one is that doesn't require the $200 tax) barreled shotgun secured to the bottom of a rifle be a legal modification? The only issue I can see with legality might be the lack of stock, but it's secured to another rifle so that wouldn't be a problem. I've seen a dual feed .223/12 gauge Crossfire MK-1 at Anthony Arms so apparently having both a shotgun rifle hybrid isn't illegal either.

In regards to why I'd want to try this, if you have to ask you wouldn't understand. I guess the best excuse I can think of is I'm a weight lifter, I like a good heavy gun, and the 75 round drums just aren't doing it for me anymore.