I'd check in with Northern Air Cargo and see what shipping arrangements they have between Alaska and your home. NAC is the standard shipper to and from the bush up here and accustomed to shipping lots of meat and hunting gear.
The waxed boxes are called "wet locks" by folks up here and very common in fishing ports. Best for long shipping are the ones with styrofoam liner boxes. Next best are the ones with the mylar blanket liners. Least good are the ones with basic plastic bags for liners.
In reverse order though, the ones with plastic bag liners can be purchased flat and assembled on site, making them the easiest and cheapest to ship from wherever you buy them in Alaska to the point at which you'll be packing the meat to ship to the lower 48. Those with mylar aren't much worse, as they can be collapsed. The ones with styrofoam are expensive to ship because they have to go empty and fully assembled. The styrofoam is basically like a styrofoam ice chest.
Ship the boxes frozen freight and you won't have to worry about dry ice till it lands at the destination in the lower 48. Dry ice can't be shipped on passenger aircraft, or at least the limit is so small that it's not worth the effort. And of course, you're not going to find dry ice anywhere but Anchorage, and that's expensive too.
Least hassle may be to pay the excess baggage fees and bring it along as you head home. Probably means you have to have a stopover in Anchorage long enough for cutting wrapping and freezing, but it sure simplifies the trip home. At the very least you could have it refrigerated real good and sealed in bags, then put into the wetlocks.
I greatly appreciate your efforts and willingness to ship the meat home. Alaska has a wanton waste law that says you have to retrieve all the meat from the field including even the neck and rib meat, and in some cases the heart and liver. If you have to fly it out of the bush in multiple trips you even have to fly the meat before you can fly the hide and horns out of the field.
To get around "having to" pay the expensive shipping of meat out of Alaska lots of hunters (way too many in my book) arrange to donate the meat to soup kitchens and the native hospitals in Anchorage. The horns and cape justify the shipping expense in their books, but the meat isn't worth it. Chaps my butt.