Def of shotgun is firearm greater than 26" and barrel greater than 18"
If you reconfigure a title 1 shotgun so that neither of those lengths are shorter than it is a legal title 1 shotgun. Shorter barrels, pistol grips, doesn't matter as long as the legal lengths are retained
Now to some other issues that are at hand. If you "make" an AOW it still costs $200 with a form1. The $5 fee is for transfers only (ie. form4). So in my opinion you'd be better off "making" and SBS unless you live in a state that does not allow them. An SBS does not have to have a stock but it can so a pistol gripped short barrel could be either an SBS or an AOW depending on how it was constructed and how it was registered.
In order to make an AOW, you must start with a stripped reciever (very rare to get ahold of) or a factory pistol grip shotgun that has never had a stock. Once an AOW it can never have a stock put on even when returned to a title 1 state unless it is removed from the registry or made into a SBS.
In order to make a SBS, you can start with any stripped reciever or shotgun. An SBS can have a stock, or not, it isn't required.
Basically if you aren't transfering an AOW, it likely isn't worth it unless you just have to have it, or SBS isn't allowed and AOW is!!