I had a Browning BPS in 10 years back.
Thought it would be a good Snow Goose buster , but found its heft to much for consistent follow through.
Ran 6 boxes through it and sold it for something else.
Your 870 is more than capable of taking care of business.
Have you tried smaller shot sizes for the geese.
Smaller pellets get into the feathers easier than the larger shot.
Try that and a more open choke, like say modified or the improved cylinder if they are in close, also when leading them do not have much daylight between the bead and their beak and follow through after the shot.
And of all things equally important use good quality ammo... I personally like Federal but others will dicker... I mean differ.
Good Hunting,
Rob