Here's some personal details for color/description, mixed in with what I do for air travel.
I remove the foam cushions from my gun case and replace them with my sleeping bag and other soft stuff. I also max out the weight limit for the case with all of my heavy stuff like binos, s-scope, etc., until it reaches 49#.
I have an AA Card, so I get a free checked bag. Other cards do similar stuff. My younger 2 sons fly with me, so that is two additional free checked bags up to 50# each. I have a 120 qt cooler with wheels, and I put other lightweight stuff in it up to 50# max.
I bring a metal tub to boil the skull for the euro mount. I pack the tub as a checked bag with straps to hold my stuff in it.
My oldest is in the military and travels separately. He gets one free checked bag. We all share the same 2 guns, so one gun case for our party of four.
My carry-on bags are now as light as they can be, creating more space since they no longer contain clothes or a sleeping bag.
For carry-ons, you are allowed one bag and a personal item. Hard side bags are size restricted, but soft-sided bags are NOT.
If you bring a soft-sided bag (like a 6-7500 cu. in. hunting backpack), you won't be size restricted if you carry it on. Returning home, make it as heavy as you can with elk meat.
Returning home with meat:
Up to 5 pounds of dry ice per container.
Put a $9 cooler bag with a zipper from Walmart inside your hunting pack with 5#'s of dry ice.
Get another cooler bag as your personal item, 5# of dry ice.
One of these cooler bags carries 40-50 pounds of meat.
For our party, 4 people will carry 80 pounds of meat each. This gives us a meat allowance of 320 pounds- at no charge.