Parking Brake
DeSitter: Sorry sir but what? Parking brakes? You seriously think they would secure a battle-worn overweight troop carrier in the cargo hold of a vehicle that moves in three dimensions and secure it with a parking brake? The parking brake would be next to useless even if the vehicle was strapped in and the strapping let go. The vehicles would be parked in gear as a precautionary starting point, but that will only keep it still while the aircraft is stationary.
You don't need such a vastly out of balance rear loading condition that an aircraft can only physically exist in a vertical condition in order for the flight controls to be ineffective. if that were the case it would have crashed a lot sooner or been sat looking at the sky on the loading ramp!
The video clearly shows the aircraft was airborne and flying albeit with high alpha and limited longitudinal control, so we can assume that any load shift, if it occurred, put the CG somewhere behind the aft limit. That doesn't mean all the cargo mass was located at the tail cone!
And no it does not automatically mean that if the cargo moved aft it would necessarily move back forward again, I can see your thinking that if its broken free it can go anywhere, but there's 50-70 straps holding these things in, they shouldn't move at all, but if they so there's all sorts of factors involved that could resist further movement.
Balance is a variable condition. "In balance" is quite a narrow spectrum. "Out of balance" is infinite, but realistically for this aircraft to reach the height it did it must have been somewhere in the early stages of being out of balance... in which case it would be possible for the aircraft to manoeuvre nose down as seen in the video.
As a former USAF C-130, C-141 and C-5 loadmaster, I can assure you that the parking brake does make a difference. When transporting vehicles, the parking brake is always set. Friction has a lot to do with cargo shifting aft. However, if the five unspecified vehicles were palletized, it wouldn't matter. Incidentally, transport category airplanes are only certified for 1.5 lateral Gs (including aft) and military requirements are to tie down for 1.5Gs aft. Civil requirements are whatever the certifying agency approves. Since National is a US company, that would be their POI.