Hello Johanna, Your project is very interesting. Overleaf is a very good tool to help students to learn LaTeX, and it would be nice to provide the same tool for emacs-org-mode.
Have a look on the following links: https://www.reddit.com/r/emacs/comments/3ql5ga/online_orgmode_editor/ https://www.rollapp.com/app/emacs https://repl.it/languages/elisp At the moment, I cannot help more, but in my opinion, getting a dedicated server would be probably necessary. Best wishes, -- Joseph