I think that these "experiments" are not performable, because the goals are too remote from what is actually feasible. The only thing that is really falsifiable, is a complete theory that spits out a number as a prediction for an observation, and the observation shows us a different number, outside of all reasonable statistical and systematic errors that can be accounted for.
However, quantum theory *as a framework* will be very difficult to falsify, in the same way as local realism, as a framework, or determinism, is difficult to falsify.
Indeed, in order to produce definite numbers, one needs an entire theory: so not only the framework, but also the flesh! The interaction terms, the constituents, etc... As such, if an observation falsifies the predicted outcome, the cullprit can be the interaction (maybe we need a fifth force!), the modelisation of the constituents... It does not NEED to point to the framework.
In fact, we are currently almost living such a situation, with "dark energy" and "dark matter", in a GR context. People found deviations from what standard GR predicts as motions in galaxies, and instead of putting the framework into question (GR), what is put in question is the constituents. I'm not criticising that approach: usually one tries to save the framework and fiddles with the constituents. It is only when this proves difficult, artificial, or impractical, and a new framework is found that can more naturally explain all the contradictory data, that one is willing to give up on the framework. But for "religious believers" in a framework, there is always room enough to fiddle with the constituents to save the framework. Look at the local realists! (or the catholic church in Galileo's time).
So I don't think that a single paper in Science will shoot down the framework of QM. It are maybe 20 papers in Science, which will shoot down the framework of QM, the day that a better framework is found which can explain all these strange results. Until then, people will try to fix things by fiddling with the constituents which use the framework.