Oneounceload's experience with rifleman wanting to shoot shotguns is similar to mine. Your pic of the overalls wearing shotgunner is what we're taking about
: The shooter is shooting the shotgun like a rifle, no wonder it reminds you of your training with the M16-type carbine. It goes against the rifleman's training to get the weak hand forward on the fore-end and the elbow up.
As 1-oz noted, in the "combat" stance shown, swinging the gun is awkward. (The stance is designed to stabilize a rifle, not move a shotgun.) And, it frequently results in canting the gun (and neck), too. If you've trained with the A/M4 using open sights and a protective mask, then you know shooting a canted weapon requires an adjustment in the aim point. With the rifle, you're aware of the situation and correct according. With the shotgun, most shooters aren't aware they are canting -- they know they are missing their target, but are clueless about the cause. Time after time, I've watched rifle shooters unknowingly start to roll while swinging a shotgun -- and with the roll, their follow-through is usually cut short. We're just trying to help you avoid the same problems.
Take a look a the soldier at 4:29 and 4:48 in the Army video and notice: he's got his left arm up and the gun is diagonally across his body. In the pics from the Magpul class, you'll see most of the shooters are shooting diagonally across their bodies with their elbows up, too. I didn't notice any "short" stocks used.
On a bright note, there is shotgun shooting near Yuma. Here's a link to info on the Adair Park
shooting complex. John Gross, the Yuma Skeet and Trap Club contact is out of town, but I've been told you can head out there any weekend morning and talk with one of the members.