The minds of the non shooting public are a problem. I think it could be handled. You mention the shotgun handling many situations. On the Bill Maher show, an African American rap type when discussing these issues said - with such a ban, if I (the guest) only have a shot gun, I can reach out maybe to 100 yards but the racists can out to me much farther. I prefer to be able to reach them also.
I agree with your other points. I wonder if they are convincing. I certainly believe in equivalency in arms and common usage from a 2nd Amend. viewpoint.
The police are an interesting case as the antigun folks are also against, for the most part, against the militarization of police. There has been strong push back on AR-15s (M-16s, M4) for the police (let alone full auto guns). I can come up with city council types denouncing the purchasing of some.
Pragmatically, this led to Mini-14 purchases (not that it isn't a usable gun) but it looks nicer. The Remington pump 223 was an attempt at a nice gun. It was promoted as taking advantage of prior training with 870s but that was BS. Similarly the first Ruger PC9s were promoted as a solution to the AR appearance problem. The Hollywood shootout put the brakes on that. I recall reading a gun magazine review of the gun that said - well, the 9 won't penetrate armor but you can shoot the guy in the leg more easily with it. I note that I have a new Ruger, for fun and it is a SD gun also.
Differentiating the full auto vs. semi version of the gun is a double edged sword. I saw a Guns and Ammo tv show where two old farts were comparing an M4 and AR that looked identical. The farts were all a twitter about the former being full auto (implied evil) and the AR being semi and thus a MODERN SPORTING RIFLE and thus nice and not so dangerous. Duh, if you presented a match video and see top competitors run the AR (a friend of mine is the Flash), that difference would be trivial. Even an old fart like me (slow) can run an AR in 5 states with only 3 points down for all. So does that make the argument that we should have them because of their easy and accurate use so that even a nutty old fart can be deadly?
Making the full auto evil - wipes out any attempt to free up NRA guns. I supposed I'm arguing for a proactive presentation of why we need deadly weapons. Will the general public go for that?