I can offer different explanations that have helped me (and am more than happy to on this thread, if you like, and discuss with you, I love the subject), but probably none of them will work for you 100% unless you are first willing to live with the fact that you are not capable of explaining everything when it comes to God. That's part of having faith.
Step one in understanding suffering: First, be willing to say that God's way is so far beyond us that questioning Him is beyond us. Just have faith that He knows what He is doing.
My problem is that this is the best tool that preachers have been using since Man created religion. JUST HAVE FAITH. I know you said more than that, but that's all it boils down to. It is not the answer.
To use your human father allegory (which breaks down after a certain point, as all allegories do), when you were very little, you didn't understand everything Daddy did, but you did know he loved you, and you did trust that he was going to take care of you and make everything OK. Now that you've grown up, and remember, you might understand.
Suffering of children in Haiti is not like Daddy insisting that you go to bed at an early hour or telling you to eat your vegetables. A good Daddy only beats a child when the child deserved it. To fit the Haiti situation, would you say that a little girl doesn't understand why Daddy destroyed her bed room and her dolls, but as adults we do? Daddy wanted to make her less materialistic? No good "Daddy" does that.
That's a reason none of your arguments will sway me-I have faith, and some pretty decent logical rebuttals too. However, none of my arguments will sway you, because you (apparently) don't believe.
Kierkegaard spoke of the leap of faith. To let go and trust.
JUST HAVE FAITH, JEFF. Just have faith. Let go of reasoning on the matter. Just have faith. Did I say it enough? Just have faith.
My son, who can't swim yet, jumps off the edge of the deep end of the pool, because he has faith that I will catch him. He knows that his father loves his beautiful little boy. For an instant, he can fly! That's my leap too. And I have faith that the loving arms of a Father will catch me too.
Bringing it back to a proper Haiti analogy: Even though God holds the heads of a few children under the water until they drown to death, have faith for the rest.
Edited to add: Okay, maybe that last one was too harsh. Try this: Even though God holds the heads of a few children under the water until they drown to death, have faith for that they will have some life in the Kingdom. They suffer horribly so that others can have faith in the God who allows their horrible suffering, then everyone lives happily ever after in the Kingdom. More fairytale-like that way.