You could always keep the posting options the same and just age any question that remains unanswered or unresponded to for 30 days into a different section - 'Arcana'. Anything that remains unanswered/unresponded to for 90+ days gets aged into 'Deep Mysteries'. Once a monk responds to an item of Arcana or a Deep Mystery, that item is moved back to SoPW.
Again, there's no way to judge "unanswered", only "unresponded to". And to that end, rather than new sections such as Deep Mysteries or Arcana, all we need is another option in Super Search:
( )Only include nodes that have replies.
(X)Only include nodes that don't have replies.
( )Include nodes both with and without replies.