I have been following your discussion on chokes with interest. Virtually all of my game shooting is driven pheasant or partridge, where of course the birds are being driven towards the guns. I thus have very open chokes, True and Improved cylinder, and I use UK size 7 shot with a 28 gram load (1930 Henry Clarke 12 BLE or 1898 Frederic Beesley 12 SLE). The guns are regulated to shoot that load too, an often overlooked process.
As you say Grumpy, most of us have to compromise with our choice of gun. On the rare occasions I find myself at a high bird shoot, or wild-fowling, my compromise is to use heavier loads of 32 grams with larger shot of UK size 5. The one thing I will not compromise is using Lylavale Express Supreme Game cartridges. I find them to be super quick, consistent and smooth. Additionally, and again an often overlooked factor, I have confidence in these cartridges and I believe that helps with my accuracy too.
With this set up I find that I can pull down the birds cleanly and am equally able to do so on birds crossing, going away as well as coming towards me. I suspect that I am not alone in finding the hardest shot being the high pigeon flying down the line, saluted by all guns and seldom hit!