Thank you all for these detailed and thoughtful responses! I will be
reading the links and thinking through the other information you
posted. For now, we will plan on a 1-week shock chlorination, being
sure to measure the bleach very carefully. I also have a lot more to
think about with regard to the "softening" systems after reading
justalur's post.

These are the moments when I wonder what we ever did without the
internet. I am still in awe that I received such great responses from
an international consortium of experts in less than 24 hours!