The best way to mitigate felt recoil is to find a shotgun with a stock that fits you as perfectly as possible.
OR
Have a gunsmith cut your stock down (or add a pad for extra length) to get that length of pull just right. Too much drop in the stock isn't normally a problem with shotguns today but may be on older guns.
Bottom line is if the gun doesn't fit right and heavy loads are used it's not going to be much fun and you aren't going to shoot as well as you would if it did fit you.