"Smooshing" the muzzle

Sounds to me like it would just take the center out of the pattern. The outside pellets wound fly straight as the barrel just turns away . The upper and lower pellets are forced inward toward the center deflecting the center from both top and bottom. Very useless idea. Pellets do not flow like water. No wonder it never worked.

There are good reasons why the world has moved away from these type barrels. Nothing beats a good quality barrel with the correct choke for the job IMO.

I heard that one of the SWAT teams here in South Florida had a couple of these. As explained to me, the idea was that you could shoot the top of a glass wall/door, and walk right through once the glass dropped. I could never really believe that this would work with Hurricane glass, although it may have pre-Andrew.

This:

The old duckbill was designed for riot control back when it was OK to bounce bird shot off the pavement and hit rioters in the legs.

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Makes more sense.

If you really, really want to open up your pattern you could always switch to a rifled barrel.
https://www.youtube.com/watch?v=HnpjrRvFTLw

Sebastian... In my opinion any SWAT unit down here that had or used such a configuration was poorly trained and was not one I'd want to command or approve... My era was from 1973 through 1995 and depending on the outfit -special weapons or special response teams varied from imaginary to extremely competent... This is not a topic that was ever discussed out in the open but with so many different agencies distributed from Palm Beach south the level of competence varied widely (understatement....).

Lemay, my understanding was that they had them in the back of a station somewhere along with all sorts of other oddball stuff they had tried out or the good idea fairy had blessed them with (single shot .50 cal, etc.). I don't think anyone regularly touched them.

I've read references to this sort of modification in various memoirs of the Vietnam war era. Particularly from the book, "Point Man" by SEAL Team 2 Plank Owner, Chief James Watson. His was the "duckbill" type on an Ithaca model 37.

I can't really speak to its effectiveness, but it seems to have been a real life modification with honest to God combat use.

I've read this also.
I believe the engagement ranges were within five yards at the time. I also believe if memory serves me that they were clearing Viet Cong out of small tributaries leading up to the Mekong Delta.
The sampans would move at night and hole up in smaller tributaries during daylight hours camouflaged and resting for the next night journey, the objective was to sneak up and take out the crews while they were sleeping.
At five yards or less, I would guess it might throw a pattern that was more horizontal than vertical and "Clear the Deck".

Shotgun patterns open up a lot more quickly than many people think, especially with Buckshot. Here are some patterns from a cylinder bore using S&B Buckshot.

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Obviously the load makes quite a bit of difference. We are getting sub 1" patterns at 7 yards and sub 2" patterns at 15 yards with the Federal flight control buckshot.