It is known that cosmic ray influx increases during solar minima and
decrease during solar maxima due to fluctuations in solar magnetic activity.
I am wondering if NASA or JPL actually monitor cosmic ray flux and know this
to be true.

As I right this letter, and send my thoughts to you on this, I presume the
concentration of C14 is increasing due to the greater number of collisions
between cosmic rays and N14. Also, recently the most powerful GRB ever
recorded actually impacted the earth. Is it safe to say that these events
would increase C14 in the atmosphere also?