I'm pretty sure it happen because you make wrong implementation on orientation control.
Orientation of end-effector
There are 4 main representation of end-effector orientation which is axis angle, rpy (expanded into 6 types), euler angle (expanded into 6 types) and unit quarternion. Normal jacobian derived freshly from forward kinematic ...
Can you set up the problem so that the quantities you care about (e.g. power) are more explicitly represented? Reasoning physically, where could the power go?
Accelerating masses, including rotation
Pushing against gravity, electromagnetics, other potentials
Stretching springs and whatever
Dissipation through friction
You say "optimize power ...