Hi, I do not think it is a problem of parameter, it is likely a more fundamental problem. Though do not understand exactly what is happening I only have assumption:
The difference between the hover command and the high level commander example is that the hover setpoint is controlling X/Y velocity while the high level commander example enables Position control for takeoff.
My assumption is that the flow sensor exhibit high noise during takeoff, the position controller over-compensate, which adds noise and generates the very shaky takeoff. The velocity controller seems to be a bit more immune to the take-off noise.
One solution might be to use a velocity-controlled takeoff sequence (maybe the high-level controller takeoff command is velocity controlled?), and then when takeoff is done, switch to position control with a setpoint close to the current estimate. This should allow stable takeoff and flight with the flow deck, though I am not sure it is currently achievable with the Mellinger controller.