After posting the question, I did a ton of googles, and eventually built a plugin that displays all media for all subsites in a multisite installation. If the user is SuperAdmin, each picture is linked to it’s editing page.
The plugin is called ‘Multiside Media Display’, and available via the usual Add Plugins page in WP Admin. (Unfortunately, the plugin will not install via the Install button; that results in a ‘Installation failed: The package could not be installed.’ error….for which I am puzzled, and have posted a question about here).
But it will install if you download/install locally. And then you can look at the code to see how it is done (too much code to display here). The code includes links to info I found about the various processes used.
So, solution available (once I get past the install problem).