Hi David,
Most of the maps are built from data generated by the CuratescapeJSON plugin – not the default Omeka REST API (I think most of the Curatescape code predates that feature).
You can review the JSON output of any view by adding a query parameter output=mobile-json.
items/browse?output=mobile-json // all items
items/browse?tags=parks&output=mobile-json // all items tagged "parks"
Note that the map for an individual item (i.e. on items/show.php) is actually generated in that page template and doesn't use CuratescapeJSON.
You'll probably want to dig into the scripts and functions that create the maps for the theme. I'd start with the
mh_display_map() function. You'll also want to know how to use
Leaflet.js, which is what we use for creating the front-end maps (there are some code comments that say otherwise that need to be updated).
I'm happy to answer questions about how Curatescape works but I probably won't be able to help much with the map customizations.
Good luck and let me know if you have other questions. Cheers -- Erin