Ahhh, for right now the only way I know of finding things, aside from the three stories up on AO3, is by using the tumblr tag the foxhole court or searching it (usually same results, I think? I legit am not sure if there’s a real difference). I don’t think anything is broken up further than that, but I might be wrong? If there’s another tag someone knows of, please let me know!

nope, we’re still using that tag for everything fandom related. ao3 would be a perfect place to post all the fanfictions, but I’m not going to force the authors to push past the closed bubble of tumblr (and even more, the closed bubble of the fandom) for a 600 words drabble or something. not going to lie, ao3 would be the perfect archive, but we have too little content for now.
as for the difference between tumblr.com/tagged/the-foxhole-court (the page you see when you’re tracking the tag) and tumblr.com/search/the-foxhole-court (the page/gallery you see when you write into the search bar on the top left of the dashboard): the former lets your see more easily the latest posts, and you have a comfy dashboard-style; the latter is a gallery that shows you either the most popular (awesome for older posts that in the tracked-tag page you’d never find) or the most recent posts (which is cool to check because sometimes/often tumblr screws up and newer posts show up in the tag search instead of the tracked page), and it has this awesome feature where you can select which type of post you want to see, so if for example you want to find the fanfictions, you can select Text posts et voilà only text posts inside the tag will be shown. 
unfortunately for us, tumblr doesn’t do a very good job at handling its massive content, so a lot of stuff gets lost or hidden. that’s why it’s really useful to follow/keep track of the other foxes (you’ll find an almost complete list of them HERE), since they all reblog stuff from each other, and you’re less likely to miss something that way. 
sorry for the long post.