Its a neat idea, but..........
Here are the disadvantages (and only the ones that come to mind off the top of my head,
)
1) Sheer size! Any self loader built to handle the 2.5" .410 (let alone the 3") is going to have to be huge compared to regular handguns, most likely larger than the Desert Eagle, and this will instantly remove it from the ordinary self defense class.
2) The magazine will have to be located somewhere other than the pistol grip. That will legally make the gun an
assault weapon (note the term) in California, and some other jurisdictions. They are so fanatic about this that California even denied a teenage girl who was practicing for the Olympics her .22 match pistol, because the 5 rnd magazine was located in front of the trigger guard. Her Senator's response to a request for exemption was a compassionate "find another sport!"
3) practical functioning. The barrel would have to be rifled, to comply with Federal law, which does not do good things for the shot pattern. Although there are ways to mitigate this, it still reduces the effectiveness of the gun with shot. Also, are you thinking of making it a .45 Colt/.410 like the Judge? Big problem there. Autoloaders can be made in any caliber, and made to function properly, BUT making one able to function with two such widely different length rounds would be an incredible engineeering challenge. It might be possible, but it will take a lot of work, if it can even be done!.
Just at a glance, all I can see is a gun that is too big for CCW, no advantage for field use, and illegal in many places. Don't think you could sell too many of them, except as novelty items.