Sure, you can only find the mistake while repeating the experiments (perhaps, as someone else suggested, in a vacuum might be a plan).
I hadn't noticed the constant thrust problem you mention, I'm now recursing back through the equations I remember to try and work out why it costs more energy to push something that's already moving fast... wait, force applied was never anything to do with energy to start with, impulse/power were. Brain-fart resolved.
I hadn't noticed the constant thrust problem you mention, I'm now recursing back through the equations I remember to try and work out why it costs more energy to push something that's already moving fast... wait, force applied was never anything to do with energy to start with, impulse/power were. Brain-fart resolved.