Make sure everyone through the process knows the lower is for a pistol. But as Stryker said, make sure it says pistol on the 4473 says pistol, don't sign one that doesn't. That's where the rubber meets the road. You can do what you want but if the 4473 says rifle, its a rifle, a SBR to boot. 10 years I believe. Check out some ready made ones on places like Rock River to get ideas.
On a side note, do your homework on upper length and velocity. IMHO, a 556 needs a 11" barrel to get up to speed but do your own work and decide. The longer barrel also gives you more control.
Lastly, DO NOT put a forward pistol grip on it. Seen this argued back and forth but a pistol can only have one grip, I believe that's 10 years also.