A year later, but anyway... (sorry for bad english)
If gods have nothing in common each other, how can you call them "gods"? How can you speak of "gohood" or even "divinity" if that does not imply any common nature or essence? How can you speak of them at all (if the have nothing in common with anything, it's impossible to know them in any way)?
Also, how can be "oneness" or "unity" before "being"?
Think it a while: if you ask for "oneness", for example, you say: "What "oneness" IS? So you're referring it to "being", or better, to «esse» (I prefer the latin). That is a clear sign that «esse» is the most universal and common, and the absolute prior.
"Oneness" is not common for both "being" and "not-being", because "not-being" just is not, has no properties or nothing else, nothing in common with "being". There's no real distinction here, because there's only "being". If you say that "not-being" shares the "oneness" with "being", then you're treating "not-being" as "being", and so it's not "not-being".
It's understandable what I'm saying?

This does become complicated. If you're interested in reading a brief, accessible primer on what I'm talking about (it's called "polycentricity"), you can't do better than this: https://henadology.files.wordpress.com/2016/11/wp32-butler-pp3538-version-2.pdf

This is where I get confused with even the Catholic vision of the Trinity. If there are multiple gods and they are in relationship to each other then there is a who and a what. If they would speak to each other then they would define themselves relative to each other and as a what (god). If there is one God then he is it and there is nothing else. There is no other. Now this is where the Trinity gets complicated for me and why I felt you were describing a sort of trinity in your description of unity among gods. It seemed to me that you were describing one god represented in multiple persons all in union with one another but all individual persons.

I guess I'm not sure what it means to say that YHWH just is if it is not to say who or what YHWH is. I mean, I'm inclined to say it is true of each God that he or she just is, such that the phrase "just is" means something different depending on the Deity.

I may be wrong but I think I disagree with your assertion:
"Equating YHWH with 'is' will reduce to understanding YHWH as either 'who' or 'what' "
If YHWH just is, then there is no who or what. Who or what implies a relationship does it not? YHWH just is. We are defined by our relationships but God is not. If you eliminate all other relationships and all other beings then he still exists on his own. We use "what" and "who" to define God because we have to but it is not so for God.

Equating YHWH with "is" will reduce to understanding YHWH as either "who" or "what": to say, for example, that Poseidon "is not" will either mean little more than that Poseidon is not YHWH, in which case "is" has been reduced to "who", or it will mean that Poseidon lacks being, in which case "is" has been reduced to "what."

Would it be better to describe the Christian god as "is" as opposed to what or who? YHWH simply is "I Am". Not a what or a who but just is.

The very question of “what” the Gods are involves ontology. Beings are “whats”, but Gods are “whos.” Because the Gods give rise to and ground being, they are not any sort of “what.” In order to transcend ontology, and speak about Gods we must speak of them only as who he or she is.