So I took the liberty of searching out the rules from each for transporting firearms on their planes. See the links below for specific information. I found info on AlaskaAir.com for transporting meat and antlers as well. I noticed on several sites they addressed the transport of archery equipment also, but I only did my search for firearms.
I hope this will be helpful to everyone this fall that were lucky enough to get drawn for those hard to get tags in far off places. Personally I"™ll be hunting in New Mexico and Colorado this fall and still have hopes of getting drawn for a couple of other places.