Assuming the gun doesn't have a POI issue, have a friend go with you and load the gun and not tell you which barrel is loaded and see if that helps any.
On a Beretta over/under you select the barrel that shoots first through a selector switch on the receiver - it's not like it is going to be a surprise as you can look at the switch and see the barrel selected. On my Beretta trap gun, the selector switch is kept permanently in the "bottom barrel first" position by a set screw. In order to enable the switch, and select the top barrel to shoot first, I would have to remove the set screw.
I'm not sure I understand this suggestion if the idea is supposed to be the shooter won't know which barrel shoots first - can you explain it further?
Seems a trip to the pattern board with the chokes should sort out any aiming problem. You also have to understand and see the pattern dispersal - 70:30, 60:40, 50:50 etc. from the horizonal.