Instead of bringing your cheek down to the stock, bring the weapon up to your line of sight. It will seem strange, because only about half the butt will be in your shoulder, but it shouldn't make any difference. Be sure to keep your elbow up horizontal to the ground so that part of the butt that is contacting your shoulder is in a good pocket.
Lean forward slightly, placing the leg on the same side as your support arm out in front. Maybe the weight distribution is 60-40, front to rear.
By leaning into the shotgun, the recoil seems to be more straight back than when you are standing upright. When you stand upright the recoil seems to be more upwards than back. The worst thing you can do is stand upright which leads into leaning back to counter the weight of the gun. Recoil seems accentuated that way.