as hinted at in other threads (ex. https://forum.inaturalist.org/t/on-explore-tab-see-beyond-500-species/7129), you can use the Get Observation Species Counts API endpoint (http://api.inaturalist.org/v1/docs/#!/Observations/get_observations_species_counts) to go beyond the first page of 500 species (leaf taxa).
i wrote something to help display the API response in a little more human-friendly format.
link: https://jumear.github.io/stirfry/iNatAPIv1_observations_species_counts.html
code: https://github.com/jumear/stirfry/blob/master/iNatAPIv1_observations_species_counts.html
as an example of how to use this, if you wanted to see leaf taxa from the Moths of Costa Rica project, you could go to: https://jumear.github.io/stirfry/iNatAPIv1_observations_species_counts.html?project_id=moths-of-costa-rica.
note that i went with small photos in this wrapper just to keep it lightweight, but if you really want to see bigger photos, you’re welcome to adapt the code on your own to display bigger versions of the photos. (hint: replace square_url with medium_url and then change the styling/CSS for the images on that page.)
while i was at it, i updated the previously written Identify Species Counts wrapper to make it easier to go beyond the first page and fixed a few other minor things, too:
link: https://jumear.github.io/stirfry/iNatAPIv1_identifications_species_counts.html
code: https://github.com/jumear/stirfry/blob/master/iNatAPIv1_identifications_species_counts.html