The issue turned out to be mysql, so thanks for the heads up, utek.
For the benefit of anyone else who might have a similar setup/ conflict:
I had installed the (fresh) 16.04LTS mythtbuntu server backend with the option that other remote frontends will be accessing it. I had, not unreasonably, assumed that the installer was smart enough to create a correct configuration.
It doesn't! It omits a bind address from my.cnf, which prevented network client connections. You can fix it as follows:
sudo nano /etc/mysql/my.cnf
Check for, and if necessary add
"nnn.nnn.nnn.nnn" is the server's IP address.
bind-address = nnn.nnn.nnn.nnn
For example if the backend is on 126.96.36.199, that's what you should enter for nnn,nnn.nnn.nnn
Restart mysql server with
I note from the logs that mythfilldatabase had also fallen in a heap, which may or may not have been related to the bind-address omission. That's behaving as well now.
sudo service mysql restart
Thanks for the feed back, people.