I don't mean to pick, but did you say you have failed to kill a squirrel with a 12 gauge at "in home" distances? The last time I shot a squirrel at "in home" range with a 12 gauge it took me 5 minutes to find a cleaned out hull of what used to be a squirrel 15 yards away wrapped around a sapling.
O no, it died.
There are these railroad tracks running next to my grandparent's property. Ground squirrels make holes in the berms on either side, and along the maintenance roads. My brother and I have spent a lot of hours and put in a lot of miles walking up and down these tracks hunting these ground squirrels, as well as grouse and rabbits. We've taken about every assortment of weaponry available to us on these walks and killed truck loads of the little varmints. At one point, it wasn't uncommon for one of us to have our respective Rem M870 12 gauges. Mine is a Wingmaster with a 26 inch barrel and an aftermarket extra-full turkey choke. I've used this shotgun to take turkeys and grouse out to 40 yards. When my dad got his Mec and started reloading for the shotguns, we had three garbage bags full of hulls for him--and that was just the ones we saved. Most of the hulls were Rem 2 3/4 inch #6 field loads. My dad loaded them with 7 1/2 because he is primarily concerned with shooting clays. My brother and I have never been impressed with the stopping power of bird shot, even on these small varmints. While the ground squirrels almost always die, we find that at any distance beyond 20 to 25 feet, it isn't uncommon for multiple rounds to have to be placed on target in short order to keep the ground squirrel from squirming down his hole to die a slow and painful death. Anymore, we don't use shotguns much. A single Velocitor from my 10/22 is far more effective to a far greater range than birdshot from a shotgun. Plus the 10/22 is lighter and handier.
So when I put my experience with shotguns loaded with birdshot together with the results of others testing them against different mediums, I just don't see how anyone would trust birdshot from home defense when I have seen it fail to stop (not kill) a 1.5 pound ground squirrel literally hundreds of times. In fact, it's really the rule rather than the exception; pull up on standing ground squirrel 50 or so feet away (about the distance from my bed, though the open bedroom door, to the living room), line up fiber optic sights COM on standing ground squirrel, pull trigger, BOOMP, perfectly centered pattern visible as dust ring around varmint, ground squirrel flops over on ground and begins flopping around and pulling itself towards hole, clack-clack, drop the rest of the mag at ground squirrel, which gradually ceases movement mere inches from hole entrance, but only after squirming several feet as it takes 2 or 3 twelve gauge birdshot rounds. Or, like I said, you can just shoot it once with a .22, blow a hole you can stick your thumb through its chest on the first shot, and not have to worry about it squirming down its hole to slowly die. It's not a shot placement issue, so there's not much we can do to make birdshot any more effective.