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....
Peter: I can't thank you enough, not only for miraculously fixing my file but for showing me the trick of using Tagged Text. I can see that being extremely useful in the future.
I knew that somehow deleting the text frame would resolve the problem and I achieved that in a much more crude way (by deleting copying, deleting the whole tex frame and then pasting back in and reflowing text) . However, when I tried your method on my current file and template, it seemed to have fixed something else—perhaps a bad preference file or something? I'm not sure but, in any case, I can even unlink in other files now as well.
Again, thank you so much for taking the time to help me out with this problem
Glad it worked out.