Explosion caused tail to detach
With no tail the aircraft pitched up several thousand feet, then
forward momentum ceased and the fuselage fell like a rock
Some reports I’ve read indicated the engines were burning as the plane fell
There is helicopter video showing the scattered wreckage
I think what you describe is most likely what happened. There is an indication that the FDR telemetry does not show much about the crash. If true, your scenario would explain it. If the tail (with FDR) was separated, the data from the flight deck would cease.