OK - I give up for now. Each time after reboot I'm having to restart Postfix manually.
I know that it was working fine initially today, but after a whole bunch of install/uninstall/install/uninstall loops of Postfix and Sendmail trying to troubleshoot the email problem, the scripts that are supposed to start it running normally aren't in place. I've tried to reinstall Postfix, but at this point it isn't replacing the scripts correctly.
This is where it's clear I'm an amateur at this, as what I'd like to do is start over, rebuild the server with this new information in mind, and then know that it has been clean all the way through. But it's probably more expedient for me to figure out somehow to get it to restart on its own. Putting it in rc.local was not good enough.