Hello Peter,
Just about the possible approach using another server's database, maybe more details are needed in order to decide if we can use "just" HTTP Clients (and HTTP calls) or if we need something more like a WebSocket server. This last allows to establish a bidirectional connection between the app and the server, and, allows to the app to receive information in real time, that is, by server demand.
So yes; certainly a WebSocket can do something like that... but I am not talking that there is something easy, maybe can be more easy than appear. On the other hand, a WebSocket server requires a dedicated hosting, and, I don't know if this can be suitable for you or not.
Said that, maybe we can avoid the usage of a WebSocket, just by consider various things, of course. We can start to know that the app's have an "Online" / "Offline" events, thant may we can use. So we can imagine that an user add an item to a shoping cart, and, if they are online, the app can made just an HTTP call to the server sending the cart' items, for example.
Once that is doing, any other app can "request" the cart' items to the server, of course. I feel that I place here just some few words, probably we must consider other things too, but, certainly probably it's possible to use the local storage in combination with a "traditional" server's database (any one, MySQL, PostgreSQL, Oracle or any other, since we made HTTP calls, and receive JSON (for example) the app is completely abstracted about the server's language nor database.
You can try to start with that approach, Peter, and, as now, we can try to help you in some specific problems. On the other hand, this do not mean that we end with PouchDB, that is, the problem right now is that I can see the app that you zipped without errors, so, I can't see what can / must be solved... if possible...