I don't have a clue what a game processor will do for you, but I have flown with meat that I processed myself. Bought coolers (hard plastic ones, styrofoam wouldn't physically make it past the check in conveyor belt), put dry ice in them wrapped in newspaper and inserted meat. After I checked them in I wrapped duct tape around lid and around cooler so it can't pop open. Last time I went overweight with my bags and got charged $75. I think every airline is different with what they charge for overweight bags, you will want to look into that if your flying your meat home with you.