Why go back a few decades? Why not simply go back to a world war they just finished fighting -- WWI?
In that war, the military used 20" shotguns. Seems to me that if the barrel was less than 20", certainly if it was less tham 18", its military "significance" would be questionable.
"and even at the time were in use by police"
Did the Miller court bring up "police"? Why are you?
But before that war, the military used much shorter shotguns, especially for mounted troops. The only thing the longer barrel gives you is more rounds, and that only if the shotgun uses a tubular magazine under the barrel. If, as a few do, it uses a box magazine, then the long barrel is a downside, for example when exiting a vehicle or clearing the inside of a building.
Did the Miller court bring up "police"? Why are you?
Just to illustrate why the military generally, but not always, preferred longer weapons, once repeating shotguns came to be. When the most you got was two shots before reloading, and the length of the barrel gave no advantage in that regard, the military preferred the shorter barrels for the same reason the police continue to do so. The military too has bought shotguns with shorter barrels, as you well know, since evidence of the Navy buying 17" barreled, Mossberg M500A1 shotguns has been posted to you before.
Remember that the Miller ruling, to which you allude, just indicated that no evidence had been presented that possession of a shotgun having a barrel less than 18 inches in length was militarily significant and that the lower court should not have taken judicial notice that it was or could be, rather than ruling that it did not have such military usefulness.
The Army is currently fielding a shotgun that is much smaller. It can be mounted under an M-4/M-16, or used stand alone in two different configurations. It uses a 5 round box magazine, thus not needing the long magazine tube.
The barrel is 7 3/4 inches long. From Strategy Page
The LSS (Lightweight Shotgun System) weighs less than three pounds ( 2 pounds, 11 ounces) and has a five round magazine, versus three for the earlier, nine pound, "Masterkey Breaching Module." The LSS is a 16.5 inch long, 12 gauge shotgun and can be operated right or left handed. ... A stand-alone version weighs 4 pounds, 3 ounces, is 24 inches long (with the stock collapsed).