The issue isn't your choke or your shell or your shot. Its hard to kill a goose DOA with a front on or side body shot using anything less than hevi or high density shot.

The key to this, much like shooting a turkey, is you need to shoot them in the head.

I like to shoot #2 or #4 STEEL for decoying geese. Just think of a goose's head like a clay bird and you'll start dropping them like rain. Remember too that they are flying right much faster than you might think. Its hard to do, but try and take your time and make sure you are following through.... if you swing out in front of the head but still shoot back, then you are probably aiming and not swinging..... seriously, its easy to get trapped in to, and it happens to me too frequently unless I actively think about it.

The other thing that I have had issue with and you might be experiencing the same thing, is that after the first shot goes off... the birds are all rising again. I have a devil of a time hitting rising birds.... I get in front of them... but not high enough above them. Lots of the time I'll knock a pillowcase full out of them... but its all from the tail and breast.... which does no one any good.

Best advice I got on this other than to shoot at the head is that on a rising bird if you can see it.... then you won't kill it. Start getting ahead and rising up until you blot out the head and I suspect you'll start killing them dead on the spot. Good luck.