You can do that, but it isn't an AOW anymore, its an SBS. There is a difference between an AOW and a SBS.
AOW is a shotgun that NEVER has had a stock or long barrel, it was designed and sold as basically a pistol shotgun from the factory. Tax stamp is $5 dollars on that.
A Short Barreled Shotgun is a long gun that has had the stock and barrel cut down after leaving the factory. Tax stamp is $200 on that.
I haven't been pricing AOWs other than old ithaca auto-burglars for a while, so I don't know what they are going for, but you need to be aware the tax schedule is different for the two.