60 something tons of vehicles moving just a few metres back wold still be quite a CG shift. Alternatively, if ballast must be carried towards the front of the aircraft then that breaking loose could have the same effect. Presumably the ballast would be carried as far forward as possible to minimise the dead weight required, therefore raising the risk of it sliding backwards a significant distance.
A couple of other thoughts, from experience of flying helicopter underslung loads, are that load weights may be incorrectly declared. When lifting a vehicle declared at a certain weight, it was not unheard of for the vehicle to be loaded with cargo of its own and the true weight to be way over what was declared. APCs leaving Afghanistan could well have been filled with kit to send home.
Although apparently a sector had successfully been flown in this load configuration already addition of fuel particularly to the outboard tanks of the swept wing would shift the CG further rearwards. An inaccurate loadsheet may not catch the error, and then you're in trouble even with load shift.
Still shocked to see such a large aircraft fully stalled like that. Those that are saying the pilot had pitch and roll control, hence the nose coming down and wings being level at impact are dreaming. It probably had more than 45 AoA at impact and was flying like a brick. A further 3000ft probably wouldn't have been enough.