Thanks for your patience.
Turns out there’s not a straight-forward way to do exactly what you’re asking. Therefore, an alternative idea to modify the map view JS to avoid the initial Ajax request is to alter the result of it (i.e. alter the query that is performed when the request is processed).
By using the wp_ajax_tribe_geosearch and wp_ajax_nopriv_tribe_geosearch hooks — early, like priority 5 — you could completely override what we do.
Or you could use those to listen for the request and then hook into the various event query actions to modify things there.
Or you could use the tribe_events_ajax_response hook to alter what comes back.
Hopefully this is enough technical information for you to get moving forward on this.
Please let me know how this goes for you.