FlyingForFun
That's very interesting! So according to you, you can make an engine produce more power by lowering the nose of the aeroplane?
I think you'll find that the extra energy you get when you lower the nose comes, from gravity (potential energy), not the engines. Your error comes from not considering all the forces acting on the aeroplane. It is true that "power" (rate of energy conversion) is proportional to force multiplied by the velocity in the direction of the force, but you must take into account the sum of all forces acting on the body, not just the engine thrust.
The bottom line is that an engine operating at a given speed and air pressure/temperature eats fuel at a known rate. Subject to the efficiency at the operating conditions, there is only so much energy the engines can get out of that lump of fuel, no matter how much power you think the aeroplane is expending. If you look at the problem in these terms, you will see that for a given set of environmental conditions, constant thrust equals constant power
developed by the engines (as opposed to used by the aircraft).
It may help if you consider just the engines and the air flow through them. An engine dumps out hot air behind it at a rate that is independent of aircraft speed. If you want to use your power/thrust/velocity equation, apply it to the mass of air that is being propelled through the engine.