Update
Last night I started following the documentation, code and database tables. I got things as far as having my menu item show up in the admin Configuration menu. I will follow this through until I get it working correctly. Since the addition is simply a matter of custom configuration settings, the original mainly used existing Zen Cart functionality (i.e. to set values for configuration settings), so this should not be particularly difficult.
I still do not quite understand the mappings from the configuration and configuration group tables to the current mechanism, but that looks like being a matter of reverse engineering.
I then suspended that work for a while to investigate SuperTracker. The original version that had been installed under ZC 1.3.9h was 1.0. It has since been updated to version 1.1, purely to make it work with ZC 1.5.x. I downloaded and installed it. It appears, as best I can tell, to be functioning all right (and the Admin Configuration and Reports menus have SuperTracker menu items in them).
So, the bottom line appears to be: Read this FAQ — https://www.zen-cart.com/content.php?309-upgrading-addons-for-compatibility-with-v15x — which also alludes to the changes being required for core admin modifications.