Hmm, how about this?

Each new note has a visible & editable text field containing the count, which increments by 10 (or whatever) each time.

Note A: 10
Note B: 20
Note C: 30
Note D: 40

So when they want to export the image and need to rearrange the notes (whether it's new notes or deleted ones), they can enter anything between the number for both notes and it'll be sorted ascendingly at the end.

So to push Note D between B & C, they change the number to something between 20-30. And there's more than adequate space to move other notes in between the two (and recursively)...