The only thing I disagree with you is your assumption I would Disagree! Really, Mike, you have to get some help.
I think the reason your long barrels pattern tighter, all other things being equal, is that the velocities begin to drop off as the powder completes it burn in the first 16 inches or so, and the shot load has to travel another 4 feet or more to escape the barrel. I think hte shot also gets a chance to " settle down " to stay together at speed after that super launching it suffers when the gun is fired, even with black powder. It repacks together in a looser version than existed with the wads were tamped down at loading, and any oscillating of pellets in the barrel is over before the shot leaves the barrel. That leaves the shot to only deal with hitting the air at the muzzle when it leaves the gun. By its nature, air delivers an even amount of resistance to all the pellets- at least those at the front of the load, behind the overshot card.
Since, I believe, the shot is pushing that card evenly after traveling down those long barrels, it most likely takes much longer for the card to separate from the shot, exposing the shot pellets to air resistance.
When you look at flight time, measured in 1,000ths of a second, and less, it does not take much of a delay in the separation of overshot cards from the shot, or shot from a plastic shotcup, for there to be marked improvements in the patterns down range.
The easiest way to look for evidence that what I theorize is happening would be to look at where your overshot cards land from a 36 inch barrel, and where his lands from his 44 inch barrel. YOu might want to use comparable loads just to make the test results more reliable. You can get the same result by simply using the much lighter dram loads given by V.M. Starr in his article on Muzzle Loading Shotguns, on Bob Spenser's Black Powder Notebook, [url]
http://members.aye.net/~bspen/starr.html[/url] using a shorter, more standard length barrel. And just to support the Late Mr. Starr as no crackpot, the Illinois River Commercial Duck hunters in the 1880s used a 2 3/4 dram load with 1 1/4 oz. of #5 shot as their favorite load to kill ducks at 50 yds! No 3 dram, or heavier loads for these guys. The article I read on this activity did not say if the guns where jug choked or not, and they may not have been. Those hunters thought nothing of shooting at flocks of ducks sitting on the water. They relied on the weight of the pellet to kill or wound the ducks, and not the pattern, I think.
However, Since I don't want to invest in a 6 foot or longer barrel, and then cut it back by inches to test this over a chronograph, I will rely on other data done by others who have sacrificed barrels to figure that out. I learned a long time ago that I don't have to jump off a cliff to know that its going to hurt when I stop suddenly at the bottom!
Historically, the Brown Bess replaced the Pike as the tool of the infantry, so the long barrel, and bayonet were essentially a dual purpose weapon for battle, allowing a volley or two of shots fired in the general direction of the enemy, and then the used of the improvised pike to repel cavalry, and later, infantry attacks. Remember that these battles were fought with the men standing literally shoulder to should, with a second rank of men ready to step up and fill the gap caused by a fallen soldier in a moment's notice. The idea was based on the Roman tactic of presenting an impenetrable human wall on the battle field to overwhelm the enemy.
I am curious about something in your loading process: Are either you or your friend doing anything to protect the shot from rubbing against the sides of the barrel as the pellets are traveling down the barrel? In my testing, I found that all the shot that had flats from rubbing dropped off in the first 20-25 yds. and did not touch the patterning board at 40 yds. I also have a good friend who has been testing shot loads, now, for more than 60 years, and he was the man who wised me up, and set up the test papers to show me where the missing shot was going, and then explained why it was dropping out.
So, I would appreciate a comment on how you, and your good friend load the shot so it doesn't rub on the barrel in those long barrel smoothbores. When I fire a load of shot containing 210 pellets or so, I like to think that more than 20 % of them will reach the core pattern at 40 yds. ( 20 inch circle)