I really don't think you guys are looking at background radiation correctly. It appears to me that you believe that because GCR is reduced by Solar Activity then a corresponding reduction in background radiation occurs. I would point out the cause of GCR reduction is the presence of Solar radiation. Solar radiation is not the same radiation as GCR but it is nevertheless radiation. It is the reason the average background radiation is so high. It is logical to assume that background radiation increases in relation to solar activity meaning that because Apollo 11 ventured out during solar peak it would have experienced ad inordinately high background radiation.
Jason has addressed this point, but I will add. The data you brought to the forum shows you are wrong on this point. The CRaTER data clearly illustrates a modulated background radiation punctuated by SPEs. The modulation of the background radiation is such that it has a minimum at solar maximum. The very fact that the SPEs are recorded informs us that the detectors recording the data do not discriminate between the outward flux of particle radiation from the Sun, and the incoming GCR radiation. They record
all background radiation levels, including particle radiation that is responsible for the modulation of the GCR, the solar wind. The radiation that you suggest raises the background considerably.
The modulation of GCR is predominately due to the interplanetary magnetic field (IMF) produced by the solar wind. This was suggested as early as 1962 (Ahluwalia and Dessler, 1962) whereby it was proposed that electric drift in the solar wind leads to convective removal of GCR from the inner heliosphere, modulating the CGR flux.
At solar maximum the solar wind *increases*, and it produces several mechanisms that perturb the IMF. The solar wind produces tangled magnetic fields that stretch out into space through the slow solar wind, the high speed solar wind speed, interplanetary manifestations of coronal transients and shocks.
The interplanetary manifestations of coronal transients form a diffusion region, the heliocentric barrier, further out in the heliosphere. This is knows as the global merged interaction region after Burlaga
et al. (1993), which reduced the GCR intensity at Earth's orbit. We are familiar with this idea, and it has been shown from the data presented in this thread.
Now, if one examines the solar wind, the increase in radiation that you suggest raises the background considerably has thermal energies (a few eV - 10 keV). This radiation presents a negligible radiation hazard to an astronaut in a space ship. In fact, the solar wind is readily absorbed by the layers of a space suit, so present negligible radiation hazard to an astronaut on EVA.
So, once again, you have hand waved you way into showing you ignorance of pertinent facts and lack all understanding of the different components of particle fluxes that exist in the solar system.