Saw the Shotgun housing at Reef Photos today. If you can imagine, having a Samsung 8.4" tablet at the back of the GH4 housing, that's how big it's going to be, except the Shogun housing is about 2.5" thick. The cheese plate tray is huge and thick. Don't think I will ever get to that point of using the Shogun. Still trying to figure how to pack the GH4 housing and tripod set up for international travel, those darn airline that weight your carry on bag!
Hand carry your housing with port. They don't weigh camera.
Sometime I even carry with tripod attached.