I don't have an in-depth knowledge of acoustics, either.....or even a shallow-depth knowledge.
Does the apparent "reduced" report occur year round, or only in colder weather during hunting season??
Have you used your Federal ammo in YOUR 16GA shotgun, and OTHER 16GA shotguns with similar barrel lengths AT THE SAME TIME, and SAME firing place? "Health & Safety" folks should be able to supply a decibel reading instrument - that you could place at a constant/fixed distance from each muzzle when fired.
If there is something unusual about your French SxS barrels' report projection, it would probably show up as quite different from the other shotguns' decibel readings.
Just a thought.
Curious. Interesting thread.