This is a trick I learned in need of a specific list. You can check in the firebug console what URL and get variable is running in the background to reproduce the result list.
The example loops over the results letter by letter and storing each unique value in an array. You probably need several nested foreach statements.
Below you see just one, which got me 200 items, going with a 2nd loop (so testing aa through zz) got me 2400 results, and I think there were even more.
The json_decode function is quite useful when dealing with data APIs which often return JSON