Well. I got almost all the way. I finally managed to get to the recovery menu. The way I did it was to go into fastboot mode with POWER/VOLDOWN. Then using VolUp and VolDown, I went to RECOVERY MODE (- VolUp and Power (pressing and holding them simultaneously and in various other sequential combinations until I finally got to the Recovery Menu (reboot system now, apply update from sdcard, etc.) This is a very useful procedure to know in any case and it took me a long time to discover it from the available descriptions.
Now the problem. I chose Apply update from SDcard and I got to a screen that says "Choose a package to install:", indicating a directory of /data/meda/0. Under that I listed not the directories on the SD card but the directories in the phone's internal memory. The package I wanted to install was on the SD card. Fortunately, using a USB connection I managed to transfer the file UPDATE-SuperSU-v2.76-20160630161323.zip, which I had downloaded, to the Android directory in internal storage. I was then able to get to it and update from it -- or attempting to. But having painfully gotten all that way, I was knocked out of the box by the message "failed to verify update signature".
How can I get past this?
By the way, I'm posting this under a slightly different name because my original account has been blocked because of email problems (messages from the forum kept getting bounced for no obvious reason).