You are right, conservation is a symmetry (there is a theorem).
The way physics manage to violate the conservation laws, the symmetries, is by changing what is conserved, keeping it conserved.
Shawyer propose that the group speed of light in a system is key, and says it changes in this cavity.
results is that to conserve momentum, which is required, we agree, it need a momentum change from the vehicle.
Energy is also conserved, making any acceleration of the vehicle lose energy in the cavity because of doppler...
I'm not convinced, but this is not violating conservation, just reframing it.
I rather support the direction of MiHsC by Michael McCulloch, which not only solves EmDrive anomaly, but also many galaxy rotation, probe anomalies, ...
I've heat that Chinese team have another theory based on Maxwell equations....
and White from NASA EW, have another based on vaccuum particles.
Each have huge critics against.
Problems is that experimental results repetitively disagree with those critics.
MiHsC is currently not finished.
people may look at the history of special, then general relativity.
For example Einstein changed many times his position on gravitational waves, from announcing them, to announcing errors, and again...
Anyway today it is more fashion to use a billion $ to confirm a theory than a million to confirm a new phenomenon without a theory.
From NextBigFuture.com --
Speculative EmDrive theory has several additional consequences.
16 Predictions of quantized inertia where experiments could validate the predictions and the theory
What the EM drive replicators should do is what Rossi has done: push the Em Drive effect power level well beyond the error bars of detection so that the EM drive effect can be reliably detected and quantified. Let's call this EM Drive+
Does anyone here knows Roger Shawyer email address? I work on a radio show called Geek Radio Kpfk 90.7 in Los Angeles and part of the Pacifica. If you know Roger Shawyer send him my email because i would like to interview him on our show.
Shoot him my email