I've checked a big duffle with my loaded pack inside, along with misc. items. Then a rifle case with pistol, ammo,trekking poles, knives, etc. Food and stove fuel, matches or butane lighters are bought upon arrival.
Last year I shipped a lot of the camping gear, along with my pack to Rock Chuck's house, and had a rolling cooler and the rifle case as checked luggage. The cooler can be emptied and filled with meat on the trip home, and its outbound contents added to the shipped package with camping gear, homeward bound. Unfortunately, the cooler came home last year packed with gear, not meat. (Be aware of size restrictions with the cooler. Also, it has to have a vent hole for dry ice if used, and you're limited to I think 10 pounds of dry ice. Also the 50 pound limit applies.)
Read their regulations as to what is and is not allowed. Most have sections specific to backpacking and hunting equipment as does TSA. I've had no issues with TSA, they've always been courteous and probably jump at the chance to inspect that case and say, "Cool, I got to look at a REAL gun today!" (Yes, I'm being facetious here.) And by the way, get your own locks for the gun case.
This isn't ideal but the best I've worked out yet.
I have a carry-on with toiletries, electronics, etc.
And by the way, I don't think shipping to Rock Chuck's house is a viable option for most people.
Point is, ship gear to a buddies house or some pickup point, ship back home at the end of the trip.