These guys were faced with a catastrophic stability issue and in a time critical situation.
Agreed.
I think the video, sadly, shows a "departure from controlled flight" with probably little to no chance of recovery. I'm sure they did pretty much everything they could with the controls during the short period they were airborne but it ended in extreme AoA and high RoD.
A *recoverable* jet upset at high altitude is bad enough (see AF447) but, as is likely, having heavy cargo on the loose inside the fuselage at low level makes it non-surviveable, IMHO. It's a bit like making a paper dart that is aerodynamically unstable - no matter how fast or slow you throw it, it just flutters randomly to the ground. Cutting the engine power might possibly have helped slightly but who's to know?