Oh, I was just being facetious. As you say, physics has undergone multiple "complete rewrites" (not really, but yeah, aristotelian->newtonian, newtonian->quantum, galiliean->lorentz are at the very least very, very serious revisions of the way we think even if they do eat their predecessors and continue to support their successful results).
However, the law of conservation of momentum is one of those things that it is difficult to muck with, without requiring a pretty complete rewrite. If you put this thing in deep space and it just moves (accelerates) without shooting mass/energy/momentum out in some form, it would make me -- and physics -- pretty sad. I have to put it in the same category as the prior reports of transluminal neutrinos and the like. Always possible that they are true, but claims that will change everything require the most solid of evidence, and so far this is in the category of any number of famous "marginal" results that turned out to be accidents of one sort or another.
At the end of the day, of course, physics is KNOWN to be incomplete. Maybe the damn thing is acting as a darkon drive and is through a process we do not understand converting microwaves to darkons to momentum through some unknown resonance process. Maybe it is evidence for a dual universe where charge and spacetime are reversed, and the cavity somehow couples the two so it is pushing off against its shadow twin. Maybe we can make up a dozen theoretical explanations for it -- eventually, if necessary.
But for the moment it, like transluminal neutrinos, is still in the "probably magic" category pending extraordinary evidence to back up the extraordinary claim. Maybe if NASA launches one into orbit with its own solar power system and runs it for a few years, during which time it promotes its orbit in unmistakable ways. It doesn't look like it needs to mass more than a few hundred kilograms total, solar panels ought to be able to provide it with at least a kilowatt or three, so getting a thrust of around a newton should be possible. A newton may not sound like much pushing 100+ kg, but an acceleration of 1 mm/sec^2 over a day adds 84600 mm/sec, or roughly 90 m/sec, or (multiplying by 9/4) roughly 200 mph. It wouldn't take many days to make a clear, unmistakable alteration in the orbit. With modern instrumentation, I would think "one" (or even less) would suffice. Even 20 m/sec/day acceleration at a tenth of this ought to show up almost immediately.
In space, there is nothing nearby to push against. One can actually use the observed thrust itself to measure the mass of the satellite and see if it varies over time (eliminating the possibility that mass is being thrown out somehow assuming that it does not, as it should not). With solar cells with a cross-sectional area of at most a few square meters, radiation pressure is utterly incapable of producing this acceleration because you have at most Pr = S/c to work with, and S is order of 1400 W/m^2 and by the time you divide by c you have basically nothing left (as observed elsewhere in the thread).
At that point, if it accelerates as advertised, Classical Electrodynamics is dead as a doorknob, and QED is walking wounded as it still works off of CED and at the microwave level and high power, "photons" ought to be irrelevant anyway. Note well: you are converting a substantial amount of incoming electromagnetic energy directly into work "with no other effect" if it works as advertised. So even the second law of thermodynamics is going to be very sad. I'm tempted to quote Eddington:
"The second law of thermodynamics holds, I think, the supreme position among
the laws of nature. If someone points out to you that your pet theory of the
Universe is in disagreement with Maxwell's equations - then so much the worse
for Maxwell's equations. If it is found to be contradicted by observation -
well, those experimentalists do bungle things up sometimes. but if your theory
is found to be against the second law of thermodynamics I can give you no hope;
there is nothing to do but to collapse in deepest humiliation."
There's some wisdom there...