I'm not following you completely, but this particular argument seems to work equally well if you put a photon rocket in place of the EmDrive. Constant power, constant torque, but I don't see how it makes a perpetual motion machine.

When you do the math, in order to extract infinite free energy as per OP's argument, you have to get the drive up to a certain speed (think of a y=x line intersecting with a y=x^2 parabolic curve). The required speed depends on the performance of the drive (i.e. the N/kW figure), with a higher performance drive meaning a lower required speed before you can start extracting energy. For a photon drive, the speed you need to reach to extract infinite free energy is... the speed of light. Which you can't get to. So OP's argument only applies to drives which perform better than a photon drive, which naturally includes the EmDrive.

Please forgive my ignorance. If you are floating in a vacuum, how do you know what kinetic energy you have? isn't that all with respect to some other object?

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

Kinetic energy is relative to some inertial reference frame. You can pick any reference frame you want and each will give you different numbers, but conservation laws should still hold in each.

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.

In empty space yes, but space is a vacuum (mostly) but not empty.

If you are in orbit you can measure your speed relative to something else, the only that doesn't work is a privileged frame.

Yup. Simple perpetual motion machine if it works.

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?

Because if emdrive works where science says it shouldn't be possible then it becomes difficult to predict it's characteristics.

Who says it’s a constant force though?

I thought that was implied by the description of the EM drive of "X kilowatt for Y newton". But I guess the effect could indeed depend on your speed relative to some special reference frame, like that of the microwave background.

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.

Good point. Or if it is emitting em waves they would get red shifted as it sped up. (Not sure if that’s ruled out)

I don't think it's implied anywhere that the force will remain constant. It's more a proxy to the ratio of the change in kinetic energy to the energy put in.

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.

The force cannot possibly depend on the drive's kinetic energy, because the kinetic energy is based on the velocity, which is relative to the frame of reference you use to measure it. If your frame of reference is the drive itself, then the kinetic energy is always zero, and conversely it's always possible to use a remote galaxy as a frame of reference, which makes the kinetic energy (and velocity) absurdly high.

Simple answer could be that it tops out at a certain speed for the energy input. 1kw might only allow acceleration up to say 1m/s and no further.

Note that we're already moving around the sun at 30km/s. Or at 230km/s around the galactic center. Or at 368 km/s relative to the CMB rest frame...