First, before I forget (again), many thanks for your service and dedication to the Corps.
I appreciate you desire to utilize your existing training in your HD preparation, it's a very logical approach. My copy of the USMC Rifle Marksmanship manual (MCRP 3-10A) starts with the familiar line: "Every Marine is first and foremost a rifleman." The fallacy is that you are trying to apply your rifle training to a shotgun. It's been my experience that trained rifleman have more difficulty learning to shoot a shotgun than someone who's never shot a long gun at all. Disciplined rifleman (like Marines) seem to have a lot of trouble learning to "loosen-up" and move the shotgun -- their training has been to maintain sight alignment while pulling the trigger. Pointing a shotgun and snapping the trigger is foreign to their training; but, the newbie has no preconceived ideas and doesn't have to unlearn previous training.
I viewed the video you linked and found it interesting, but, not very practical in some respects. While the demonstrator talked about having the shotgun squared to his feet and shoulders, in reality he advanced his left shoulder. In order to get a grip on the fore-end, he twists his shoulder (and spine) out of square from his hips.
Having your stock so short that you can't grip it with your thumb (else you get whacked in the nose) may seem tacti-cool, but impractical. Not only is it contrary to your previous training, it reduces the recoil typically absorbed by the right hand and makes the gun easier to be taken away from you.
Access to the safety selector is moot. In a HD situation, you don't want to be messing around with a safety. The safety device is your trigger finger - outside of the trigger guard is safety on, inside the guard is safety off.
The recoil demonstration was meaningless, he was comparing two different guns. If you noticed, he was very slow and deliberate while firing a single shot from each gun. Perhaps quickly emptying the magazine, on multiple targets in motion, would have been more telling. I suspect, if the demonstrator had done so, we would have seen his shoulders become less and less square with each shot.
I still recommend an introduction to shot gunning class to learn the differences between rifle and scattergun shooting. If you wish to fully utilize your existing training as a Marine rifleman for HD, perhaps an A4-type carbine would be a better choice of weapons. Good luck with your selection and be safe.