A beautiful question! In case you haven´t found your answer yet as far as accidents in God, I´ll try to clarify it a little bit for you, according to the doctrine of the Angelic Doctor.
It sounds like you already are familiar with the idea of God´s simplicity. In finite beings, there is a real distinction between being a man and being this man (suppositum and essence), there is a real distinction between who I am and the fact that I exist; (alas, I was brought into existence and could cease to exist: being and essence); between being myself, and accidental aspects of who I am, like my hair color, my virtues, etc (substance and accidents).
In God, as you pointed out, there are only rational distinctions, which means that any distinction that we make within God is merely a cognitive device to help our poor little intelects piece together some sort of image of who He is based on what we know about Him from the universe, breaking down so much splendor into smaller rays of light that are more easy to digest.
In God, His Being = His Essence = His faculties to know and to will = His real act of knowing and willing. In Him there is only one "huge" act of knowing and willing, by which, from an eternal present, He wills, creates, and knows all things in present, past and future.
In finite efficient causes, the real relationship with whatever they produce is a mere accident; having created the Pietá was only a small spart of who Michelangelo was, however great that work of art actually is.
However, since God creates all things with one act that is identical with who He is, having created one specific creature or another gets lost in that simple act, in the same way as the ideas of all things that exist (and even those could exist and don´t) are all wrapped up and included in what it means to be Essential Being.
It´s almost like the difference between someone who learns to play a piece by Chopin, and thus participates in his likeness inasmuch as he effectively imiates his model, whereas, in the case of Chopin himself, anything he played would "sound like Chopin" in the most perfect way, since he himself was the effective, subsistent Chopin-ness, Chopin par excellance.
Thus, finite beings participate in the likeness of Eternal Being by the fact (and in the "degree", way, shape and form) that they are.