I believe the trick here is that constant-acceleration with constant power use is due to the (puzzling) particulars that there's no ejection mass
If you are in orbit you can measure your speed relative to something else, the only that doesn't work is a privileged frame.
Addition of kinetic energy is pretty unintuitive in this regard, e.g. when throwing a ball, the "work" done by your muscles depends on the reference frame that you pick to analyze the event.
This seems, to me, to be the simplest explanation of why it almost certainly doesn't work, but that isn't mentioned frequently, am I missing something?
If that's the case, then we can do something like the Michelson–Morley experiment, to check whether the effect is different depending on the direction the Earth is moving in its orbit.
I suppose they used a very precise equivalent of a dynamometer that necessarily required some work to be done to give out a reading and this is what it showed.