I'm very open to the possibility that I'm missing something important in all this. But I still don't feel like you've made any clear argument about why my energy reasoning about the fields outside of the parallel plates fails. Your initial response to me here didn't address the exterior field at all: your linked calculations (which you called "the full derivation") were explicitly just about fields between the plates, and in fact assumed the plates were infinite. You also claimed there that I had "failed to apply conservation of momentum correctly in the general case of two different masses", even though my objection had nothing to do with the mass difference.

I do agree that the non-zero field outside of the gap was the subject of the previously linked subthread. But the discussion there was about "ballenarosada"'s (flawed) estimate of the exterior field: my overall claim (and theirs!) is that the specific functional form of that field can't matter, since we know from fundamental principles that its integral (the electric potential) must go to zero at infinity. You claimed there that if one neglects plasma screening, "you get a finite contribution which can be made arbitrarily small relative to the work done inside the capacitor, where the force is constant, simply by increasing the size of the capacitor." This claim is incorrect. Again, the easy way to prove that is just to note that the electric potential goes to zero at infinity. But if you want to actually consider the electric field due to a finite parallel plate capacitor, you can compute that easily enough along the axis of a pair of circular plates. As it must be, the integral from the midpoint to the positive plate is exactly equal and opposite to the integral from the positive plate to infinity (independent of the plate radius or the separation).

Your final claim is that plasma screening means that integrating all the way to infinity isn't necessary. I'll admit that the details of that are well outside my area of expertise, and I'd appreciate hearing more about it. But my strong sense is that if the number of charged particles is finite, the fundamental result from basic electromagnetism must remain true regardless of screening effects: the electric potential at infinity must be zero. (Right??) So as I understand it, screening effects can make significant changes to the shape of the potential curve, but regardless of those details its values at the plate and at infinity remain unchanged. And that's all we need to conclude that there is no net thrust for an ion that doesn't change direction (like the ones that the author claims will produce thrust).

In particular, if we imagine a positively charged plate in a plasma, I can easily imagine a negative screening charge accumulating right next to the plate, which would in a very short distance bring the exterior field to zero. But at the same time, that nearby accumulation of negative charge would strengthen the field right next to the plate, almost like a second parallel plate capacitor. The effect would be that positive ions outside of the positive plate would be strongly repelled, and would in turn push the device in exactly the opposite of the claimed direction of thrust.

I'd love to learn more about the plasma physics of this situation. But I'm less interested in the specific details there than I am in understanding anything that would interfere with the basic energy analysis that I've outlined here and above.