Can you prevent a specific subject category (with associated items) from showing up on the subject list?
Absolutely! You just need to modify the API URL slightly.
Where 1,2,3,4,5 are the IDs of the subject categories you want to exclude.
That produces this list:
Finding category IDs: Go to http://yourlibguidessite/cat.php and click on a category; note the cid in the URL.
Have you assigned a friendly URL to a category? Never fear! Just remove that, look at the URL, jot down the ID, and add it back.