Thanks Dave. By the way, a different thread up here is from a group of people who believe that they have solved this although their solution didn't work at all for me. Take a look -
Outgoing mail server gone under El Capitan
You'll see towards the end that one of the posters has them all using iCloud's outgoing server for everything, and apparently that helped these people:
"OR_CDOct 2, 2015 5:07 PM Re: Outgoing mail server gone under El Capitan
Re: Outgoing mail server gone under El Capitanin response to DrasticbunnySolved
Had the same problem, icloud emails were still coming through, but somehow el capitan deleted outgoing icloud server.
Solved by going to System Preferences > iCloud > disable mail option, wait a second then re-enable it.
Went back to Mail app, hit send on iCloud outgoing email and the outgoing server list popped up.
iCloud was back in the list, select and "always use this server"
Worked for me."
As I said, this didn't help me at all, actually messed things up, but so many here seem to like it that maybe there's something of value in this?
P.S. And since you said to keep Mail's Preferences open for now, I assume that also means to keep Mail open 24x7?
Larry