Have used free walk in freezers in an Anchorage motel for freezing game before a trip home. Worked great for Caribou, Halibut, and Salmon. We shipped it home on a one way flight on AK airlines, they stored it in a refrigerator after landing, I got it two days later frozen solid. For the Caribou used the waxed cardboard boxes, seems 50-70lbs in each, the ones purpose built to ship frozen stuff in. Been a few years... I know there are options in Anchorage, do not know about Fairbanks, but odds are a motel, meat processor or a cold storage locker could be found. Ask your outfitter or transport service?
A Moose is a whole different deal. That is a bunch of meat. I love Moose and would bring as much home as possible. Can be costly and depending on how you pack it, may take several days to freeze. What we did with the cardboard boxes is fill just it about 1/2 full, then take the lid and turn it over and fill about it up about 1/3 full, maybe a bit more but under 1/2, then spread out the packaged meat to freeze faster. 24 hours in a zero degree walk in and it was all frozen solid. The boxes we got had lids that reach all the way to the bottom of the box, gives 2x insulation on all 4 sides.
I had gallon freezer bags I placed the disassembled meat in. Just be careful to try and freeze them in shapes you can fit in your box... Used about 1/4" - 1/2" news paper on the bottom of the box and crumpled paper to fill the little space left at the top. Bottom paper helps insulate, but if there is some thawing, will soak up fluid and keep box from leaking for a bit. A leaking box can be problematic in terms of commercial transportation. We duct taped the heck out of the boxes and off we went.
I've also packed my gear in 2 70qt or so coolers for the trip up. Then used a couple light nylon duffle bags to ship most gear home UPS, and my meat in the coolers. Where there is a will there is a way. Good luck!