Well, those videos sure have no relevance with the thread at hand,
No your problem is you are fixated upon one set of conditions and applying a solution which will probably suffice under those specific conditions to a large set of situations in which that solution will fail horribly.
The 12 gauge slug produces approximately 3, 000 ft pounds of muzzle energy. Under 50 yards it will punch through the shoulders of a bear like they were butter. It will flatten out to more than an inch in diameter while it does.
The 30-06 180 grain nosler shooting at 2770 ft per second generates about 3,000 ft pounds of muzzle energy it will open up to about 50 caliber it will also break the shoulders of that same bear. In either case you have a quick follow-up shot. In 3 seconds with the shotgun or the 30-06 you can unload 9000 foot pounds of muzzle energy on that bear.
In either case whether we're talking about a 30-06 or 12 gauge shotgun we're talking about more than 10 times as much muzzle energy as most medium bore airguns.
Sure you can do it with a slingshot under exactly the right circumstances with perfect conditions and a little bit of luck. That doesn't make it advisable.
6600 I have looked at the pictures of your arrow shooters they are impressive and I am sure they would do a humane job on a bear but if that bear had any possibility of charging me I'm going with the shotgun.
Admittedly some of that has to do with the fact that I was a bow hunter for many years and I have encountered black bear on foot alone in the words at very close ranges while only armed with a bow or a fly rod. I hasten to add I was unwilling to take a chance on pissing the bear off.
I don't think you get any chances to kick a bear out of a blackberry patch by accident in the Hawaiian Islands do you?