Bonus round: Dani and I tested this with my linked answer earlier, by changing my footnote to [3] instead of [1]. Didn't help; it displays and acts like [1], with this bug in force.

I'll hazard a guess that the problem is that whatever renders the Markdown to HTML sees only one post (the question, or a single answer) at a time. So the ID numbering starts over at 1 for each new post, resulting in multiple #fn1, #fn2 and so on anchors in the document tree. A brute force solution to that might be to simply patch that code to use GUIDs as anchors instead of numbers, but display numbers. That'll probably break external links to footnotes, but I think we can live with that.

If I were doing it, I'd patch the code to be #{post id}-fn{id} and #{post id}-fnref{id}. Easier to read than GUIDs and you probably have all the data already at your fingertips. With editable posts, I don't think GUIDs would necessarily even stay consistent. Whether you seed the GUID from the order of footnotes in the post or the text in the footnote ID ([^this]), both can change in a post edit.

I don't know if there's a way to rewrite incoming link-anchors from the (current) system to a best-guess new anchor in this new system.