If it is ineffable, then, calling it literally non-dual is literally incorrect.  Even calling it simultaneously both dual-and-non-dual is incorrect.  Itt sounds as if the words "literal non-duality" have no meaning at all if they are being used in place of "ineffable".

I think possibly the most important statement that has been made in this thread, and perhaps can ever be made about this topic is what ends the quote above:

"he was persuaded to teach ... by pointing out to people that their lives were unsatisfactory and that there was something you can do about it"

"pointing out to people that their lives were unsatisfactory"  <---- projecting failure on others ...

This is very important because this explains the projection of failure on anyone who is not in the buddhist "club".       It does.  Thank you.  I did some writing outside the forum to organize my own thoughts on this.  My goal was to solve the contradiction myself using my own methods and talents while temporarily setting aside my own biases.  In other words, I set aside my opposition ( which is contrasted with denial ) in order to sincerely try to solve the problem.  In doing so, what I developed is in large part matching what you wrote.  Also, in a fun bit of irony, it matches what Stirling wrote too.  The ideal "solution" to the contradiction is using a model of dissolving "duality" into "non-duality" just like a salt-water "solution".     From this, it can be stated without contradiction that there is a "non-dual" awareness which is acheiveable and superior to a "dualistic" awareness, because the non-dual is including the inherent dualism ( or more accuratley, multiplicity ).  All of the benefits that come from buddhism seem to be retained by speaking of non-duality in terms of awareness and nothing seems to be lost.  I'm curious if you agree with this.  Is there anything lost by speaking about non-duality in terms of awareness?  Maybe it's helpful to consider the two-truths doctrine, since that's what prompted this thread.  For the two-truths, could the cup's simultaneous reality and non-reality be considered a non-dual awareness?    
    Same question as above.  Is there anything missing from the benefiits coming from buddhist practice, or are there any contradictions or conflicts in buddist teaching is the word "reality" in the above quote is replaced by awareness?   ? "Buddhists would define the non-dual awareness as the mind of the Buddha" ?   Does that ^^ work?  Are there any problems with that statement from a buddhist perspective?  If Buddha is not teaching ontology ( did I understand that correctly? ) then, where is this assertion about reality coming from?    "Reality is the mind of Buddha?"   <--- this is a truly bizarre assertion.  I'll skip that for now.      Agreed.  And this is precisely where I ended my own contemplation on a non-dual awareness.  I used the terms dissolution and resolution which are happening simultaneously.  You're using the word co-emergence to describe this simultaneous phenomena which is interdependent.   But if this is extended into a descriptorr of reality, it cannot be non-dual.  Similar to the chain metaphor, what happens if either Purusha or the Prakriti are removed?  Reality ceases to exist.  This guarantees that both Purusha and Prakriti are significant individually.  This is confirmed by considering reality where there is only Purusha or only Prakriti.  It would be a very different reality from the reality where they are both co-emerging.  Because of this, reality MUST be dual.   And this resolves the contradiction.  Non-dual awareness is consistent and logical, non-dual reality is not.  This naturally requires the cabability to distinguish between one's own awareness and reality which is exceeding beyond it.    What do you think?