Sorry to reply to myself, but just an update....
I have left avast! with that one box of the Behavior shield unchecked and that has clearly solved the issue. As it had recurred sometimes after a few days, I had this fear, early on, that the problem would show back up, but it hasn't.
Today, avast! support replied to the ticket I put in earlier. Basically, they said there will be changes to the Behavior Shield in avast! 7 and that I should wait and see if that resolves the issue. I understand that.... With a new release coming out, no need to try to fix a problem in the soon to be old version....
That does bring up a question. Things I have seen in these forums and even the tone of the support reply indicate that there have been some problems with the Behavior Shield being imperfect. So, has the Behavior Shield had issues? I am not asking to complain, but rather trying to find solace that other had issues with that shield as well...