I have run thousands of rounds of 20 ga. through a 6 lb. 5 oz. double gun on doves in Argentina. The doves there are certainly not driven but are traveling in a straight line, which usually is towards you, so the result is the same as driven birds, whether pheasants or doves. The point of the question here is not about the quarry, but the load and the gun.
So, here's the facts. I ran an average of 1300 rounds per day (6 hours of shooting) through my Beretta 687 SP II Sporting, which weighs exactly 6 lbs. 5 oz. with extended choke tubes in place. It weighs exactly 6 lbs. 3.7 oz. with the Beretta flush tubes in place. I shot 7/8 oz. loads 90% of the time, with the other 10% being with 1 oz. loads. One morning I drew a stand that presented very high incoming doves and the bird boy had provided 1 oz. loads in anticipation of this. I shot them for a while, missing the high doves badly. I finally figured out that I was leading them too much. When I cut my lead back they started falling like on the other days. I told the bird boy to go get me some 7/8 oz. loads and lose the 1 oz. ones. With M and an IM chokes I went back to a high average with the 7/8 oz. loads.
The only ill effects I experienced from this high volume was a very slight tenderness in my shoulder pocket which was totally gone the next morning. Four days shooting in a row. I experienced no recoil related issues with the 1 oz. loads that morning. I just had to figure out the lead. Extra payload won't make up for poor shooting.
Take home . . . . . I see no reason why a well fitting 6 lb.+ gun can't be used with 7/8 oz. - 1 oz. loads in a large amount. That said, we don't all have the same tolerance for recoil. So, adjustments must be made to accommodate for that.
