Yep, if it wasn't for the AWB, it would be no big deal to have an SBR that was also regarded as being a "pistol". Just get your carry permit if you didn't have one already and go have fun.
If the firearm can fit the definition of a "pistol", then the criteria for Evil Assault Weapons are different and it makes it tough to come up with a legal SBR. Does your magazine attach without going through the pistol grip? Does it weigh more than 50 oz.? Oops. Does it have a fore end? Oops.
Think about putting together an SBR that has no more than one of the following features:
(B) A semiautomatic pistol that has an ability to accept a detachable magazine and has at least two of the following:
(i) An ammunition magazine that attaches to the pistol outside of the pistol grip;
(ii) A threaded barrel capable of accepting a barrel extender, flash suppressor, forward handgrip or silencer;
(iii) A shroud that is attached to, or partially or completely encircles, the barrel and that permits the shooter to hold the firearm with the nontrigger hand without being burned;
(iv) A manufactured weight of fifty ounces or more when the pistol is unloaded; and
(v) A semiautomatic version of an automatic firearm