I really enjoyed your response to my last response. Following is a quote addressing your question about Aquinas' terminology. The rest may not be wholly responsive to your point, but it's what I've got right now.

From Aquinas, Thomas and Ralph McInerny. On Being and Essence. Thomas Aquinas: Selected Writings

We must take a moment to backtrack and examine more closely the terms that Aquinas uses in the quote above. What are rendered as “to exist” and “existence” above are in Latin represented by esse (“to be”). When Aquinas speaks of “being as being”, in Latin he writes, “ens qua ens” (ens is expressed as “that which is”). It is difficult to render the difference between these two terms in English. Another attempt, by Dr. Walter Redmond, renders ens as “being” and esse as “be-ing”. The difference is subtle, and does capture some of the difference in meaning. It does not, however, quite capture the difference between the uses of the two terms. In his commentary on the De Hebdomadibus of Boethius, Aquinas says, “First he says that to be (esse) and that which is (ens) are different. This difference is not now to be referred to things, of which he does not yet speak, but to the notions or intentions themselves. For we mean one thing when we say ‘to be’ and another when we say ‘that which is’, just as we signify one thing by ‘to run’ and another by ‘runner’.

Part f the Tsongkapa distinction is that "existence" does indeed carry the implication of, in the terms of this discussion, God, or in his presentation. the word" existence" carries with it in unexamined usage and experience the modifier "inherent". This is the illusion or delusion.

In this approach things exist/appear as the unity of "mere clarity and awareness" . So the becoming of the rock, it's becoming clear to perception, and awareness together, simultaneously, is rock as "what is".

The "monotheistic idea" reminds me of Aquinas' characterization of God as "existence alone". Only God is this, everything else is existence and some particular nature that define and limits it.

The paradoxical method of much of Buddhism is dominant in Zen and some schools of Tibetan Buddhism. Tsonkapa's project was to use reason to avoid the recourse to paradox. This is what lead to his refinement of the description of Emptiness.

I'm not sure what you mean by "the transitive-existing of the rock". Is it either the rock's share of existence endowed by God limited by it's nature, or the rock as process, arising and ceasing according to how causes and conditions line up, or am I not getting it at all?

In terms of my recent-ish Buddhist-y posts at AG, perhaps the question of What is God can be reduced, as an exercise in reduction, in the spirit of experiment, to the idea, (or the imputation of the idea onto whatever appears), that anything at all exists inherently, that is, in an independent non-contigent way. In which case, God becomes as much as Self, the object to be negated.

God then becomes the hoped for irrefutable faith/proof that things exist the way they appear ie inherently existing, having an essence, a soul, that things are things. God then becomes the disembodiment of our own individualized vivid experience of consciousness.