Fuzzy anchoring is really about addressing a different problem than the one faced here. Fuzzy anchoring handles the case where you know what the current document is, but the content of the document has changed since it was annotated. In this case the problem is that the client doesn't know what document(s) (tiddlers) are visible or how to change which ones are displayed.
For applications that do client-side navigation we can probably implement a general solution for "good citizens" that update the path of the URL to reflect the current document/page as the user navigates. TiddlyWiki doesn't do this by default, although I see there is a setting  which will make it update the fragment. The client currently ignores the fragment, as it identifies a subsection of a document rather than the document itself in "normal" websites.
If someone could make a variant of TiddlyWiki that used the path in the URL to represent the current document that would make it easier to support (although that would also complicate deployment). Otherwise I suspect we'd need a custom "integration" (like we have for PDFs) that understands TiddlyWiki specifically, or some heuristics to determine that the fragment identifies the document rather than document section being displayed.