What you describe is a point of impact issue. Different loads affect barrel time and recoil in a SxS gun, thus causing latteral POI change. How tight you hold the gun to shoulder and face is also a variable. The heavier shells obviously suit your shooting style best in THAT gun.
A quick shooter can break trap birds with a cylinder choke but statistically he will not break all of them. A 70% pattern at the target plane assures a possible 100 straight, a 50% pattern assures frequent misses. This is an established fact.
Also, the time of flight difference between a heavy and light trap load only allows the target to travel an additional three inches or so, hardly enough to move it out of a cylinder choke pattern. The pellet energy difference at the target plane is near nil.
Swing the gun through a pattern plate using your standard trapshooting technique with various loads... see if I'm not correct.
