Do I think there’s an “unbridgeable chasm” between what St Thomas and the Catholic West have to say about God as pure Esse (“being”) and what St Dionysius and the Orthodox East teach with regard to the Divine as a Hyperousia Thearchia (“supra-essential Godhead”)? Is there a conflict, in other words, between Being and Beyond-Being?

Not at all, but I fear it would prove a lengthy distraction from “the one thing needful” to try to develop an answer, as your question seems to intend, in historical terms. What I can tell you, on the historical side, is that the Angelic Doctor quotes the Areopagite more often than he does any of the other Fathers, with the single exception of Augustine. He at least must not have thought there was “chasm”.

In lieu of such a scholarly answer, perhaps a brief note from Schuon will suffice:

“When it is said that the personal God is situated in Māyā, which runs the risk of sounding offensive, one must be careful to make it clear that this God is the Supreme Principle ‘entering’ into universal Relativity, hence still ‘Supreme’ despite the ‘entering’, which enables one to affirm that God the Creator and Legislator is at one and the same time Ātmā and Māyā, or Ātmā in Māyā, but never simply Māyā” (“The Ambiguity of Exoterism”, In the Face of the Absolute).

My sense is that you’re feeling a bit constricted by Thomistic formulations and categories, which you wish to do full justice to despite your evident affinity for perennialist metaphysics. This feeling is understandable. The presence of Māyā in divinis cannot but frustrate those who wish for their terms, and the corresponding realities, to stay put. We must be willing to say, and then unsay, if we wish to honor the “fluid” character of the Real.