Energy transfer - Kinetic to Potential
etang,
You posed the question: "If the cargo shifted during takeoff roll, or on rotation, how did the plane manage to reach the altitude seen in the video?"
What appears to have happended (cargo shift or not) is that the airplane rotated to a very nose high attitude and climbed sharply. What took place was a transfer of the kinetic energy the airplane had built up during the takeoff roll into potential energy of altitude gain. Going back to basic physics here are the equations for Kinetic Energy as a function of velocity (feet per second) and Potential Energy as a function of altitude (feet).
Kinetic Energy = 1/2 mass * velocity^2
Potential Energy = mass * gravity * altitude
With these units gravity is 32.2 feet per second squared.
Using these two equations and solving for the altitude increase that would result from converting all kinetic energy to potentail energy yields:
Altitude change = Velocity^2 / (2 * gravity)
If the velocity at rotation was 150 knots the equation above yields an altitude change of 1000 feet. If the velocity at rotation was 175 knots the resultant altitude change works out to be about 1400 feet.
It is not at all surprising that a 747 would climb to about 1200 feet if following takeoff rotation the crew was not able to keep the nose from pitching up to a very steep angle leading to stall. Keep in mind that the engines were continuing to add energy during at least a portion of the climb.