I ended up not getting to doing the web server backup until much later than I had intended. I ran into some problems with the installation of PHP 7.0 that didn’t cause operational problems but did slow down the server somewhat as it attempted to load library extensions that were already compiled in. This was the result of the machine having been upgraded from a previous version that did not have them compiled in but the upgrade did not automatically remove them from the configuration file.
So server is now at the most recent version of everything in the long term support release (I am not upgrading to 16.10 at this time both because it does not seem to offer any significant operational enhancements, and because I have experimented with it on a non-critical machine and found it to be buggy still).