CHSH (2-channel) for instance doesn't count for a case where all 4 channels didn't detect anything (simultaneously) at some point in time. As I understand, such all-absence shouldn't happen/matter at all in QM-theory (maybe except Pilot-wave equations, not sure) and in any way shouldn't matter in practice (given that practical loopholes are closed), as it wouldn't carry any information about particle's measured state (as, maybe a bit oversimplifying, it is carried by by +1/-1, not zero's).
But still, are there experiments that are actually aimed at getting timestamp (like per planck time more or less) of arrived particle, but with (at least basic) loopholes closed? I have no other restrictions here, so GHZ-experiments, Leggett-Garg (and others) could be taken into account too, or even Werner-state "linear" entanglement without violation. My guess any such test would require a lot of energy for a clock but maybe there is an elegant way to do that?
As an additional question: in overall theory of QM, should we count for a case when nothing (no particle, no energy) is measured on every [possible] side/channel/measurer when computing correlations? For instance, in original double-slit temporary "absence of particles" wouldn't change diffraction pattern at all, as pattern can still emerge over time... some modern double-slits even seem to show that even predicted absence doesn't affect "emerged" statistics (as putting an obstacle in "dark fringes" changes nothing when both holes are open).
P.S. The reason I'm asking is that such (hypothetical?) time-sensitive experiment would show (and explain how exactly) relativity of simultaneity doesn't affect resulting statistics. From what I could google, it seems like even time-bin entanglement measurements require [co]incidence monitor.