Shot placement is King, penetration is Queen. All else is gravy. Shotguns kill by having multiple pellets of sufficient size penetrate deeply enough to shred vital organs. Animals die from shotgun wounds in hunting situations not from an energy dump as in maybe a high velocity centerfire rifle cartridge but because large amounts of vital tissue is destroyed by multiple pellets and is no longer functioning. I might add that rifle cartridges also need to accomplish the same goal but that they do so by a different means. Because individual shotgun pellets lack the high velocity energy, diameter and construction of rifle bullets it requires multiple pellets to get the work done. That's why patterning is critical. You just can't rely on the single Golden BB to get the work done.
In the case of a sled to capture or record momentum or energy dump for shotguns I doubt it would be very impressive at 40 yards. I don't think it would give a true reflection of a shotguns killing power. Much in the way of an arrow and broadhead. An arrow launched from a modern bow has very little energy on target. But it kills game dead very quickly and humanely because momentum drives that razor sharp broadhead which cuts a large hole through heart, lungs, arteries and veins disrupting their function. Animals succumb very quickly and quite humanely to deeply penetrating sharp broadheads. I've shot through deer while bowhunting and they often have very little reaction to the shot. Maybe kick slightly, hop off a few yards and look around like they were stung by a bee. Within short seconds they get wobbly and go down. Usually they move off from the shot from 25 to maybe 100 yards and are down very quickly.
In the case of shotgun pellets my concern is how large the pellets are, are they large enough, material of construction, how deeply can the individual pellets penetrate and how far can I get a sufficient number of those pellets to impact at point of aim? This be it dove, turkey or coyote. Range is a factor because it limits penetration of smaller pellets and also limits the number of pellets in the kill zone with larger shot sizes. This is due to the considerably fewer pellets in the load and increasing pattern spread. Every ten yards past the forty yard line really penalizes the pattern. Choosing a suitable load and working out reliable patterns to point of aim is critical to success with shotguns. Especially so on larger animals. All the yelping about 70 - 80 and even 100 yard shotgunning is well and fine but you have to hold reliable killing patterns in a 10" circle at point of aim. Plus the pellets need be of sufficient size and penetrate deeply enough to shred vital organs. And that's a challenge that nobody seems to be able to consistently accomplish. It's the question that the yelpers can't or won't answer. Hits on a plywood coyote cut out in the gut or hind leg don't count. Relying on the Hail Mary that Uncle Ernie used to kill that one coyote at 90 yards back in '77 from his bolt action long tom goose gun doesn't count either. It's what is consistently and repeatedly going on in the center of the pattern right at point of aim that counts. Otherwise you're praying for the Golden BB. Can I kill a coyote with a dove load of 7.5 shot? You bet, but the coyote has to be a lot closer than if I'm using Number Four Buckshot. A bit of a rambling thought on the subject. It's been discussed here numerous times in the past but I'd bet it's yearly one of PM's most often discussed and cussed topics.