Last Sunday I shot 122 pigeons and a crow with a Henry Egg hammer gun. Using Winchester Western 32g No.6 and Game Bore Pure Gold 28g No.5 shells - 294 in all between 11.00 and 16.00.
Felt a bit kicked around by the end as the gun is short for me at 14 1/4". Generally not too bad though. Your problem is poor gun fit and/or mount.
Lesse if we can translate "The King's/Queen's speech here" 5 hours and about 1 dead bird for every three shells fired in an Eggbeater Limey hammer gun. Back when John Olin tested his new M21 with those 2000 blue pill over loads, assuming 1000 rds. per each tube- which of all the fine doubles made in the World was the first to "give up the ghost"-- Not a Parker, not a AH Fox, not an Ithaca NID-- British guns are made for light loads, when I go after barn pigeons and crows, I use AA 12 Trap loads of 1 & 1/8" oz. no. 8 shot-- and I can shoot 'em all day long in 7 lb. 4 to 12 ounce weight American shotguns- But would not want to try that with the lightweight Limey guns often with overhoned and extra thin walled tubes--But, if you go with Nash Buckingham's "The Dove" taking one bird for three shells pass shooting with a wind factoring in, not too shabby a performance. Pip[ Pip and Cheerios, Olde Boy!!!