Consider this graph if you will. Is is the same graph that performing a median of the data would provide. All the data is lined up numerically from high to low. If GCR was the dominant component you would expect the curve to be flat with a sudden upstart to reflect the SPE component. The curve is not flat. That suggest the SPE component is the major contributor to background radiation. It is also of note that the lowest readings do not suggest a low enough value to have supported a lunar transit.
My bold in your quote, as I want to address that point.
1) The curve won't be flat if the GCR is strongly modulated, will it? The background GCR flux is modulated, so it rises,
won't it?.
2) The peak at the end is due to SPE radiation events skewing the data. The SPE event contribute the most by
magnitude, but temporally the background radiation is predominantly due to GCR.
Your attempts at analysis to step around the issue are quite unremarkable in that you are simply presenting the data in a different way and it tells the same story. You r new graph clearly show there are periods of time where the level is below the threshold, the rise GCR rises for less active parts of the solar, and is skewed for sharp peaks due to SPE events. Remember, this was
your initial premise. I being deliberately tautological here.
There are prolonged periods where the GCR flux is below the threshold you stated, in every graph you have presented. That was your initial argument, but in any case you can dismiss the CRaTER data. Please refrain from discussing it again as it does not apply to the solar cycle 20.