Success! (at least in part!) I developed a plugin, mapped all my sites to a single set of NGG tables. All four sites can now “see” all of the galleries. Here’s something I can’t do:
If I insert a gallery into a post, AND THEN TRY TO SHARE THE POST WITH ANOTHER OF MY SITES, I get an error message that the gallery is invalid.
The text that is inserted looks like this: <img class=”ngg_displayed_gallery mceItem” src=”https://fortwayneata.com/wp/nextgen-attach_to_post/preview/id–492″ alt=”” data-mce-placeholder=”1″ />
The problem is that the 492 is a hardcoded index into the “post” table of the originating site. The other sites can’t reference that table.
One solution would be to use a shortcode that reference information in the shared ngg_gallery table I just set up.
I haven’t carefully explored linking a gallery to a page, but it appears that the link is to page ID, which is also unique to a single site and has no (or wrong) meaning to the other sites.