This is a slightly different approach to firearms protection -
1. Get a standard canvas "soft case" like -
2. Get a "Tuffpak" (designed for large camera tripods) -
When traveling, stuff your gear in the Tuffpak alongside the soft case to keep the rifle from shifting around. You will probably want the soft case at your destination, anyway. Use the Tuffpak for the return flight and stash it somewhere (possibly a rental locker) during the hunt.
I find the soft case provides sufficient protection for rifles behind the seats in a pickup. That location protects them from the "heavy gear" in the bed.
However, they don't provide adequate protection from airline baggage handlers. That's what the Tuffpak is for.