Singleton Custom Field (Meta Box)

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Storing of your own meta fields is typically a custom process, more so if you are using a third party framework.

Technically it’s possible, but clunky:

  1. Hooking into save_post would allow you to check if meta is added to it
  2. If so you can immediately query for previous (if any) post that had it and unset the meta for it

However I concur with the comment you got that this does not essentially seem to fit a purpose of post meta well. There are precedents in core itself (for example front/posts page handling) to store such things as post’s ID in an option.