I think the Loader Model is a more direct path to what you are describing. In most cases it does not break with any observations that I saw.
The "accuracy" is probably the same, depending on how the experiment is setup. Even a standing clock can give the accurate time, once a day. ;-)
But, the experiment that are directed towards detecting this variant, show that the Loader model is valid... due to double detections of quanta, when there should only be one. According to the experimenter that I linked to, with easy-to-repeat experiments.
So Occham's razor tells me to look into it, before starting more complicated theories. It is not my favourite theory, but I am a scientist.
I had a small discussion setup here. Feel free to add a comment. https://saidit.net/s/Physics/comments/18rz/nullhypothesis_qu... (saidit is a friendly community for open discussions)