The Casimir effect already produces perpetual motion (in that sense.)
Which raises the specualtive question of whether the Emdrive exploits the Casimir effect to obtain a tiny thrust (in which case a drive subdivided into a vast number of really small trapesoidal sections might produce much more thrust.
You misunderstand the Casimir effect. It's a relativistic analogue of the van der Waals interaction, with a very curious alternative derivation from zero point energies. It is not free/negative energy, it is not free momentum, it was never a controversial subject, we only didn't have the practical means to measure it.
Exploiting the Casimir effect can't give free momentum, because the derivation of the force is rooted in quantum field theory, which like any other physical theory of the last 400 years contains conservation of momentum at its very core.
There's a simple way to get free energy out of a working em-drive: "at some point, the kinetic energy of the device-driven mass exceeds the energy input, and if this energy is collected via decelerating the mass (via regenerative electromagnetic braking, for example), then there would be a net gain in energy." How do you get a net gain in energy out of the Casimir effect?
Vibration is continuous. Free energy you can get - whether we'll ever harness it to obtain thrust or electric power I don't know - but endless minor amounts of heat, yes.
How do you produce vibration with a force that makes two metal plates stick together? Once they're stuck together, the force goes away. There's no repulsive Casimir effect, and insofar as they bounce, they will quickly come to rest. It's like trying to extract free energy by dropping a ball to the ground.
Let accept that there is Ether, and Ether is like water. In such case, Casimir effect may depend on the flow of Ether, so if plates are in free space and exposed to unbound Ether, then Casimir effect may happen when plates are oriented perpendicular to flow (as usual), and may NOT happen when plates are parallel to flow (my prediction).
The Casimir effect was both predicted by quantum field theory and observed to behave more or less exactly as predicted, so there's very little room for supposed etheric effects. If they were observable, we probably would have seen them just by accident already.
But Ether Wind was disproved by Special Relativity theory, not by Quantum Theory. I see no conflict between Quantum theory and Ether theory. But, if you wish, let accept that there is Quantum Field, ...
The conflict is simple: quantum fields are conservative, which means you can't arrange mass/energy in one way, and then rearrange it another way, and end up with more energy than you started. Gravity is conservative: if you drop a ball, friction aside, it will bounce back into your hand. It can't go higher, and there's no magic you can do by arranging matter to come up with a path where it ends up with more energy than it started with (unless you steal the energy from elsewhere).
Any such effect that exists, would not be called the "Casimir effect" because it would have to obey completely different laws than the actual observed Casimir effect seems to. The Casimir effect is actually evidence against such an effect, insofar as it's perfectly explainable in terms of conservative forces.
I see no word "Ether" in your post. LIGO (which is basically Michelson–Morley experiment at much higher scale and precision) already demonstrated waves in Ether/QF(Quantum Field)/PV(Physical Vacuum)/Space caused by merges of black holes, so I see no point to play this word game anymore.
I'm unsure about why you think that laws of conservation will not hold for Ether, AKA Quantum Field, AKA physical vacuum. If we will be able to get energy from QF, QF will lost that energy and will cool down, so Casimir effect will be smaller until it will vanish. However, there is no shortage of PV in space, and Sun is pretty good at heating it.
However, because of wave-particle duality, and because waves are propagating without moving, and because waves are propagating at speed of light, Casimir effect may be unaffected by rotation even when exposed to raw vacuum for speed less than 50% of speed of light.
Which raises the specualtive question of whether the Emdrive exploits the Casimir effect to obtain a tiny thrust (in which case a drive subdivided into a vast number of really small trapesoidal sections might produce much more thrust.