The Brits in "Merry-Olde" experienced (as I have read) that driven pheasant/grouse situation so often they made up guns just for such a scenario. The right barrel (front trigger) was choked tight, and the left barrel (rear trigger) was choked more open. They apparently fired the right barrel first at a distant target, then the left barrel was fired second as another closer target was about to pass over the gun.
About two years ago I passed up an offered Cogswell & Harrison 12 gauge SxS so configured, as I already have enough variables in my shooting life without adding reversed chokes.