While this is an EXCELLENT idea, I must warn you that you are moving into the realm of NFA. A short barreled rifle has a barrel less than 16" while a short barreled shotgun has a barrel less than 18". Unless you dont mind having your 18" barrel stick wayout in front, go ahead and mount up. There are also Any Other Weapons (AOW) that are a $5 transfer tax (Serbu super shorty is one) that are a shotgun reciever that has never contacted a full stock in its existance, only pistol grip. DO NOT buy one of these and put it on an AR15. Once you do that you are firing it via the shoulder stock of the AR and have an illegal SBS. That is a ticket to Club Fed. You might be able to get a virgin receiver from Remington or Mossberg that has never had a shoulder stock that you can make into an AOW, but it will cost $200 and be put on a Form 1, for that route you are better off buying an SBS and you can also put a full stock on it. If you desire the shorter version, you will have to get an SBS and pay the $200 tax stamp. The NFA forum has more info on this mod, I got this info from my Class III dealer when the same thought crossed my mind. If you want to do it, go for it!
When someone asks you, "Why do you want to mount a shotgun to an AR15?" your response should be, "WHY NOT??" or "You just answered your own question!"