Jettisoning load isn't really throwing away energy, because the load will also consume energy in a proprtional sense.
Consider your answer for b - trade speed for height. Speed gives kinetic energy, which you are proposing to convert to potential energy. Which gives height.
Kinetic energy is 1/2 * mass * velocity squared.
potential energy is mass * gravity constant (g) * height
So the height you gain for a given speed change is given by m*g([delta h] = 1/2 * m * ( [start speed^2] - [end speed]^2)
"m" is on both sides of that equation. All of the kinetic energy for any incremental mass goes into providing the potential energy for the same mass. Mass is, for this exchange, a wash. There's no benefit, in energy terms, in retaining mass.