I've been thinking some more while I ate dinner, and while it doesn't address why the unlink option isn't working for you, the following procedure should accomplish the same result:
Make a backup copy of the file, just in case.
Make sure that linking is disabled for text files in the document currently.
For each story that you want to unlink, place your cursor int tohe story, select all, then export to InDesign Tagged Text (verbose or abbreviated is OK). Delete the text, but not the frames holding it (that's why you selected all). Place the Tagged Text file you just exported back into the threaded frames.
Repeat the process for each story....