Dear Jeffrey,
The question you are raising - “Why does  Levinas so much insist on the radical division between the times of memory and  the immemorial time?” - is really a central one. Your article is a good reason  and, in a certain way, a challenge which gives me an opportunity to sort out  the solution I myself have been looking for.
The dichotomy between the assembled into the  whole of Being - either by individual or collective memory, on one hand, and  the immemorial, on the other, which is not just what is forgotten, but is what  has never been memorized, what is not memorized, and what could not be  memorized, is correlative to all principle dichotomies that Levinas introduces.  A huge gap separates: 
1) 2) Immanence - Transcendence Essence - Beyond essence Being - Otherwise than being I - Other Archē - An-archical Ontology - Ethics Cognition - Good etc. 
In the Levinasian construction, the terms in column 2 have acquired a double status. When inside the Totality they are opposed to their logical/dialectical oppositions (in column 1), they receive a meaning through their place in the System of worldly interests. However, besides these meanings through the reference to the illuminating totality, they take on meanings in a dialogue. Then, all these contents are “animated with metaphors, receiving an overloading through which they are born beyond the given.”