I took a cursory look at how Twine handles hooks in JavaScript. You’d need to replace the hooks for SaveGame, LoadGame, and SavedGames (list of saved games). You’d need to add some type of login that Twine respected. For a professional JavaScript developer, this is probably a week or two of work (including design, testing). The login aspect would require some type of authenticating back-end, but the rest could remain client-side.
Similarly, building something similar for FyreVM-Web would be slightly more complex, since the saved data has to be stored somewhere…LocalStorage may not be appropriate for Inform-based save files. It would need a relatively complex back-end server to handle processing. I’d estimate a professional JavaScript developer would take two to four weeks to implement something sound with FyreVM-Web.