But the energy of the spacecraft is not static. As the craft falls towards a body it is trading gravitational potential energy for kinetic energy. Thus the fuel

But the energy of the spacecraft is not static. As the craft falls towards a body it is trading gravitational potential energy for kinetic energy. Thus the fuel/reaction mass gains kinetic energy along with the rest of the craft. So at the lowest point to the body that reaction mass has the most kinetic energy. From here it could go two ways: a) The craft does nothing. The full mass continues to get higher and the kinetic energy the reaction mass gained is turned back into gravitational potential energy. b) The craft ejects (maybe by burning) the reaction mass. The kinetic energy of the reaction mass is transferred to the craft. Ejecting the reaction mass slows it down and that speed is transferred to the craft. Now the craft continues with all the energy it had going in, but because it is much lighter less of that kinetic energy is transformed back into gravitational potential energy. Or think of it this way. You have a big rock at the top of a hill. You roll that rock down the hill and convert 100 units of energy in to kinetic energy. At the bottom of the hill is a see-saw. The big rock hits it and launches a small pebble. That pebble still only has 100 units of energy, but it's moving much faster than the big rock did. It is not about getting more energy, it is about shedding mass at the right time to transfer (what starts as gravitational) energy from the fuel to the craft.