Whatever God does is, by definition, right because there is no standard, outside of Himself, by which He is to be judged.

It's called the standard of Good and Evil, and God subjects himself to it by defining himself by it.

Good and upright is the Lord.

-Psalm 25:8

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it is quite another to begin to accuse Him of wrong and think that we are competent to judge the Infite, the Eternal, the All-knowing.

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God himself admitted we have a god-like understanding of Good and Evil. We weren't supposed to, but we do. It's why we fell, remember?

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Then the LORD God said, “Behold, the man has become like one of us in knowing good and evil. Now, lest he reach out his hand and take also of the tree of life and eat, and live forever—”

- Genesis 3:22

So yes, you're right that we can't know the mind of God, but what we DO have a godlike knowledge of is Good and Evil, and I can judge any being by that standard.

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If I objected to hell being just, I would be like a child screeching, "That's not fair!" when confronted with situations and actions of adults that I simply do not understand.

Nope. I can look at the action of creating people for fire and say "that seems evil to me" and that judgement would hold weight. Again, I have a knowledge of Good and Evil like God himself, so I am an expert on the topic. God said so.