The paper itself details a range of mundane error sources (including thermal expansion) that still haven't been ruled out as the cause of the observed thrust.
How do you know that?
Consider a pretty simple and obviously correct device: an electric engine with an internal rotating shaft + a solar panel to power it, floating in space. The faster it rotates, the higher its acceleration in the gravitational field.
Conservation of momentum only works because the gravitational field itself is supposed to have momentum. Similar to how momentum is conserved for an accelerating paddling boat only if you include the sea. Sea analogy is a good one I think, especially because the gravitational field interacts with itself, like water, contrary to electromagnetic fields.
Well, you're right that it's not a mathematical certainty that momentum is always conserved.
But there's such a mountain of evidence for it that we should have a very high bar for claims that it's violated. Thermal effects and measurement error are both likely sources of the discrepancy.
But another reason to be skeptical is that Noether's Theorem tells us that a violation of conservation of momentum is only possible if the laws of physics are not translation invariant, and we should be able to use the violation of conservation of momentum to illustrate a specific instance where physical laws are not translation invariant. That would be Earth-shattering. (But not, strictly speaking, impossible)
While I agree with your statement I derive the opposite conclusion from it. (I.e. these results are certainly false and you can see what that implies about economics and social science.)
So far the thrust results have been replicated more than the majority of economics and social science research (i.e. more than zero times).