Being one of these hard headed framers, I build my own shipping containers. If the frames are particularly expensive or you are shipping framed art, it is a very inexpensive and safe method to ensure that your pieces arrive in one piece.
I build the carcass out of the cheapest 1x4's that I can find or rip down larger one x stock to the size that you need. You can miter the ends on your chop saw and join them with PVA glue and bugle head screws. For the sides I use either double thickness cardboard or thin masonite. Every box of foam core has a large sheet of double thickness cardboard in the bottom box and I use a box cutter to cut away the sides and store the bottoms in a closet until I have a need for them.
You can cut them to size on your wall cutter and use PVA and either staples or 1" bugle head screws to attach them. I put one sheet on the carcass, a layer or 2 of bubble wrap in the box until the frame is centered, then place the frame into the box, and fill with more bubble wrap until it is all snug in the shipping box. You can fill around the sides of the frame to keep it from shifting around with strips of bubble wrap and then glue and screw the top on the container and you are set to go.
I have been using this method for quite some years and haven't had any insurance claims to date. It does require a bit more work but that hasn't killed me yet and I enjoy building something that I know will get the job done.
Framerguy