Try to pack all your gear into a duffle bag and then put it inside a big cooler. Check the cooler as on e piece of luggage and then check yyour rifle as your second piece. On the way back, you' ll have to pay for teh extra peice of luggage (the cooler full of meat) or you can have the cooler shipped overnight. A little riskier in my experience. The airlines will typically allow you to check teh trophy as long as it' s packed right. Can' t have no sharp points stickin out. Bubble wrap and duct tape work wonders for this.
Call your airline, They get you lined out!!
Good luck!!