Yeah, over 50 cents per shot for .22 birdshot is crazy, especially since it isn't very effective except at short range. Keep that stuff in a revolver for snakes at spitting distances. A better pigeon solution would be to buy a good accurate pellet rifle, and snipe them when they settle in to roost in the evening.
I have a scoped spring piston RWS model 45 .177 cal. that makes 1000fps and is very accurate. And I also have my old Benjamin model 347 .177 cal. pump type pellet gun that is still very accurate after firing untold thousands of shots. The power of the Benjamin is variable depending on the number of pumps, up to around 750 fps. Either one will easily kill pigeons with less noise than a .22, and minimal cost.