There are many differing opinions from hunters and Outfitters regarding taking meat back into the United States from hunted animals. There are a 2 steps you must follow but basically yes you can do it without any problems.
Have your meat cuts prepared and labelled by a licensed butcher
Declare your meat when entering the U.S on arrival
How New Zealand Safaris accomplishes this is after you have harvested your animal, the guide will cut and carry out the meat and transport it back to the lodge where the meat will be cleaned and trimmed. From there they take it to a butcher to be processed, wrapped and labeled. They then collect it and freeze if required, when the hunters then leave put this in a purchased small cooler bag that will fit inside your main carry on. The main cargo hold in the plane is not heated on the flights so being inside a cooler and wrapped means the means maintains a cold temperature and will not leak.