Kalam

[Belacqua]

But the simultaneous existence of things, under Thomism, is not causation but simply coexistence.

The way I see it, under Thomism, a cause is based on an essential relationship. If the relationship is accidental then it would be, as you say, simply coexistence. Early in this thread @Belacqua accurately described this critical essential/accidental distinction in Scholatic nomenclature.

Your interpretation of Thomism is different that ours. I do not think the dispute rises to the level that justifies accusations of ignorance. 

I think I'm going to give up on the word "cause," because it is too misleading to modern ears. 

From now on, I'll translate "the αἰτία of X" as "that which must exist in order for X to exist." Or, because that's too long, I'll say twmeiofXte. As a sort of abbreviation. 

So if twmeiofXte must exist in order for X to exist, then it is clearly not mere coexistence. The existence of X depends on twmeiofXte.

One more example before I give up: 

Hydrogen must exist in order for our sun to exist. Therefore hydrogen in essentially prior to our sun. If all the hydrogen in the universe disappeared, the sun would also disappear. Conversely, our sun could disappear without all the rest of the hydrogen in the universe disappearing. Therefore the sun is essentially posterior to hydrogen. 

Hydrogen is twmeiofXte where X is the sun.

I am not optimistic that this explanation will suffice.

Also I realize that it's kind of odd for me to post this to you, since you are the only one here who already gets it.