quoting Dr. Dick:
"I am of the sincere opinion that everything cannot be explained."
As John Hospers says: ultimately things just ARE. Seeking an explanation of an ultimate explanation would cease to make it ultimate, so would be a contradiction.
Since "ARE" refers to "EXISTENCE" WHO Christians call "God"; ultimately you are face to face with "EXISTENCE" (God).
"No matter how deep an explanation goes, something is in effect being assumed"
Yes, you are assuming "Existence" (involving "law of non-contradiction").
"That is an intellectual dilemma and is indeed my definition of god: the Great Original Dilemma!"
So our definitions of "God" seem to correspond, except that there is no dilemma.
"That is by definition something not understood and anyone who claims to understand any aspect of it is lying for any valid rational explanation of any part of it immediately becomes part of "that which can be explained" and is thus no longer part of the Great Original Dilemma!"
But you forget: God is a living conscious BEING, He incorporates self-referent UNDERSTANDING.
You have not defined "explanation". You have not shown that "the assumption of 'validity' itself is not valid. You assume "assumption": what is assumption? Define that?
This all leads to the idea of just call a spade a spade.
You say "by definition" something "not understood"; but you are not defining "by definition" or defining "understood".
By saying "by definition" you broke your rule as you assumed an understanding of "understanding", of "assumption", and of "definition"?
How about define "explanation", "valid", "rational"?