"The Fourth Way argument goes as far as to prove that there must exist a being whose essence is moral goodness to the maximum degree."
I agree that Christians attach the label "God" to the entities that Aquinas reaches at the end of his Ways. But the Fourth Way does not argue that God's essence is *goodness*. It argues that there is something that is maximally true, maximally good, maximally noble, maximally existing, and from the further premise from Aristotle that the maximally true are maximally existing, we are left to infer that the same X is maximally T, G, N and E. It goes on to conclude that this X is the cause of EG and "of any perfection whatsoever" [cuiuslibet perfectionis] for all entities. Nothing is said about X's essence's being identical with its existence. (That thesis, by the way, is not argued for in the Second Way, as you said above that it is. The Second Way is an argument about first efficient cause.) In your OP, after all, you wrote "And these beings are called perfect because they have goodness of that nature to the maximum degree ..." or there exists a being such.
More argumentation is needed to demonstrate that if X is maximally good, X is Goodness. I should think that the Fourth Way does not argue that X is goodness, but rather, that X is maximally Good and causes other, subordinate beings to be good. X has the property maximally but is not the property itself. The 4th Way concludes with this claim, that X is the cause of goodness for all entities. But if X just is good*ness*, then Aquinas would be concluding that X is the cause of X, i.e. of itself, for all entities. Given that X turns out to be God, I don't know how one could that God is the cause of God for all entities, since God is uncaused. God exists necessarily? But that's not the point of an argument from maximum degrees of properties.
I don't think the Fourth Way is that great. It's not demonstrated that maximal truth, maximal goodness, maximal nobility and maximal existence are distributed over the same x; we only get a citation from the Metaphysics that what are maximally true are also maximally existing. It's not clear whether properties that don't fall into Aquinas' list of transcendentals (nobility is generally not put on that list, BTW) also get distributed over the same X. One might think that they are not so; e.g. in the case of hot, which Aquinas uses twice as an example, the maximally true/good/noble/existing entity is not also the maximally hot entity. I think here of Parmenides' question about hair, mud and dirt, heh heh. So the "cuiuslibet perfectionis" premise would be false. Further, if "the maximally F is cause of F over all x's" thesis does not hold for all values of F, then the 4th Way seems to fail to establish a universal cause.
Finally, there is the old "existence is not a perfection" problem.
I think the argument in the De Ente et Essentia is stronger than the Fourth Way, though it too gets tangled up in making existence a perfection. In the ST, at any rate, it is only in 3.4 that God's essence and existence are argued to be identical. So one is not authorized to use "God's essence is identical to God's existence" as a premise in the Ways back in 2.3.