As to the bunching phenomena you postulate, all you have to do is give me a specific scenario and I believe we can explain why this does not apply.

Quantum mechanics (from Loudon):
The typical quantumoptical experiment produces one or twophoton excitations described by a spatial wavepacket, with some degree of localization. The wavepacket function is expressed as an integral over contributions from waves with a range of frequencies, or wave vectors. We treat the fields as classical quantities and impose the quantization only on the field energy.

Hypothetical bunching model:
Photons are localized with a diffuse external field and a single frequency. By themselves they do not have sufficient energy to cause a detection event, but the superposition of fields of many photons leads to intensities sufficient to cause a detection event. Detections are caused by the superposed fields of photons.
Starting in 1965, Bell and others constructed mathematical inequalities whereby experimental tests could distinguish between quantum mechanics and local realistic theories. Many experiments have since been done that are consistent with quantum mechanics and inconsistent with local realism. But these conclusions remain the subject of considerable interest and debate, and experiments are still being refined to overcome ‘loopholes’ that might allow a local realistic interpretation.

It is thereby assumed that realism can be defined by a mathematical analysis of experiments. Don't you think that this is presumptuous? It seems more likely that realism is more fundamental than quantum mechanics. The problem with quantum mechanics is that it only accepts challenges to its interpretations that abide by its rules. In the Nature article there are two objections to violations of the Bell inequality: that there is a subliminal communication and that not all detections were recorded. It does not suggest what to me is the real cause, that the detection event is incorrectly interpreted. Bell's inequality is a commentary on the nature of detection events, not locality or photons. Clearly we cannot look behind the phenomena to determine the truth, but as long as that possibility exists local realism has not been disproved.
It seems that it's reasonable to assume that the quantum theory is an incomplete description of physical reality. And that the incompleteness of the theory, in a certain sense, can be deduced/inferred from the theory itself. But, afaik, when people speak of the completeness of quantum theory they don't mean that it's a complete description of physical reality (After all, how could anyone ascertain that  what might it refer to?). Rather, what they mean is that the quantum theory incorporates everything that's known about reality via quantum experimental phenomena.

Quantum mechanics should be able to say what part of reality cannot be observed, IOW precisely define its own limitations.
You believe that singlephoton model somehow implies nonlocality but bunching model implies locality.
Well, I do not agree. Singlephoton model by itself does not conflict with local realism.
On the other hand Bell theorem applies to your bunching model just as well.

The trouble with trying to prove quantum mechanics wrong is that they insist that you come up with better predictions. All one has to do is prove that the predictions are based on a superficial understanding of nature or photons or whatever. If Bell was using an incorrect model then he is proving something about quantum mechanics, not reality.