On my AK. trip two years ago, I had my moose processed in Anchorage and then shipped to CO. in freezer boxes. Cost me about $.90/lb. to ship. I only had about half the meat shipped, left the other half for my sister and brother-in-law to eat in Anchorage. Also had the taxidermist work done up there, and then shipped down, that cost me more than the meat did. It took about 3 days for the meat to get here, from point A to point B, BUT amazingly it was still mostly frozen!
For the most part, dry ice isn't allowed on airlines, as checked luggage or otherwise!
Another option might be to use coolers as your luggage on the trip out, then simply box your clothing and ship it back home and put your meat in the coolers as check in luggage and take the meat home with ya, as long as it's frozen. That's the hardest part of taking the meat with you, is getting it frozen for the trip, if you don't have a couple of days after the hunt before your flight home! I guess, if the trip was quick enough, the meat wouldn't have to be forzen, BUT it hadn't better leak either!