Euthymios, I'm not the expert on anything here, but I tend to look at this issue differently. Maybe someone who's well-versed on this topic can help us out. At any rate, here's my take:
First, as Dionysios and Maximos say, God isn't a being and he doesn't properly 'exist' since being and existence imply their intelligibility. Second, the cognitive distinction between essence, that which is unknowable, and energy, that which is revealed and unites with us (theosis), is simply that: cognitive. The term 'essence' is simply a place holder for that of which we can know nothing since it is beyond our capacity. If saints were to be united to the divine essence in theosis, they would be God by essence. The distinction between essence and energies is only problematic if they are defined as parts of a whole, as in something created. I think your problem reared its head again when you said, "The ecumenical councils never applied parts to God -- with the exception of the members of the Holy Trinity." Here we already have either tritheism or monism. For, if "god" has three parts, then that which constitutes "godhood" is either a set of attributes that is common to three individuals (which is implied in speaking of the three hypostases of the Trinity as parts), which is tritheism, or, if the three hypostases are truly to be united in a way other than common attributes but are regarded as parts, then the three parts, or hypostases, are simply three emanations of an impersonal essence. Since God isn't being and therefore isn't subject to predication according to created terms, then only that which God reveals about himself can be relied upon in order for us to understand him. Photios' Mystagogy of the Holy Spirit is all about this problem as it is manifest in the filioque. When we think of God as ontologically absolutely simple, as the Roman Catholics and many Protestants do, then we run into all sorts of problems as we confuse the divine essence, energies, and persons.
I think Gregory is only telling us what he learned from the Fathers before him.