I haven't noticed it shooting low with shot before this test. Recoil was low really. I think more powder is needed and may lift the muzzles a pinch for me.I'm simply relaying my own experiences. It seems to me you are likely more experienced with fox than I am.
I did rewatched your videos, and noticed you mention your Pederosli 10 gauge shoots low. Mine did as well. Unfortunately I never did come up with a perfect solution for that. I had been shooting mine with a slip on cheek pad, but it felt weird shooting it and seeing so much of the top of the barrels.
Most of my foxes are shot with rifles but my favourite shot is #4 bird. As you mentioned shotguns don't primarily work on the chance a pellet just happens to hit the right spot ( although that can and does happen) but rather the accumulative effect from many hits. There is always a compromise mind. Pattern verses pellet count, pellet count verses penertration etcetera etcetera.
I do think a lot of folks look at pellet size and think no go bigger when under most circumstances they actually would be better with more strikes from a higher pellet count.
It is illegal for me to use buck shot on deer in the UK but I have been so close to deer on numerous occasions it would be a viable option despite what the critics say. I don't need an expert to agree with what I already can determine for myself! So come the great tribulation I guess I am somewhat ready, God willing.