I FIGURED THIS OUT - at least for me, and hopefully for everyone else.
Today my brother started to get my text messages as emails - like everyone in this thread.
I discovered he had accidentally texted me using my email address instead of my phone number. You can do that. From that point on, my replies to his messages from that text thread all appeared to him as emails with a *.txt attachment file.
To fix it: I just texted him using his phone number and he replied. New thread! All happy again. Text msgs are text messages. No email. If you have this problem, just tell the other person to text you in a new thread using your phone #. Depending on their message app, it may choose your email instead if the person just types your name instead of manually entering your phone # - so make sure they manually enter your #.
Why the Verizon techs didn't figure this out 4 pages ago?? I dunno.