On a 2 trigger shotgun, most folks go front to back, and the gun is choked appropriately.
However, some of the best shooters in the world are the live pigeon folks, with major cash awards to the winner. Many of those set up their shotguns to be shot back to front, the premise being the kick moves the shotgun back while the finger moves foreward, making it faster. Kinda splitting hairs, but they have to kill the bird within a set distance, so speed is paramount.