Thank you all for the rich theological and scriptural reflections. Here is a philosophical thought.
It seems that the problem is the following: while it is true that natural evil is only evil in so far as it affects humans or things humans care about (after all, we measure natural disasters by death toll and property damage), how could an all-knowing, all-powerful, and all-loving God allow apparently random suffering and death, especially of the most innocent among us?
One logical solution is to declare that there is no God, or at least one who does not care, does not see our plight, or is powerless to do anything about it. The unfortunate consequence of this position is to affirm that life is fundamentally unfair, that justice is an illusion, and therefore man’s most coherent behavior would be to either grab for as much power, pleasure, and possessions as he can before his life is spent, even at the expense of other men, or to give up on life and allow despair to push him into suicide (as many philosophers have done).
The second logical solution is to affirm that life as we experience it IS unfair, and therefore if justice, order, and reason are indeed real, there MUST NECESSARILY BE a God who judges each in the next life according to his life on earth. A two year old dying of dysentery is unfair. A two year old dying of dysentery and rewarded with eternal joy is quite just.
I therefore state that the problem of natural evil is not a proof that God does not exist, but exactly the contrary, a necessary proof of the existence of a just, loving, omniscient, and all-powerful Judge.
Sorry but this doesn’t work either

. Continuing with the example of the fictional Tamint, the two-year old girl who dies from a waterborne disease as does some real child in the world every minute of every day - one child dying once would be sufficient proof, there is no need for another to die every minute of every day, as if God keeps forgetting he already made the proof. Enough with the proofs already.
And anyway it’s arguable whether an injustice can be righted by a later compensation, since a toddler dying from diarrhea can never be undone. It also paints God as being powerless to prevent suffering, and only able to pay out on the insurance later.
The issue with many of the theologies expressed on the thread is that in one way or another they try to justify suffering, and that puts them at odds with our normal human reaction, that Tamint’s suffering is unjust, and we ought to try to prevent or alleviate such suffering.
Some say Tamint is to blame for her own suffering, as if karma is getting her back for sins from previous lives. Some say her parents are to blame, as if no one should have a family so long as there’s any chance their child may catch a disease. Some say we’re all to blame, as if primitive man invented viruses, bacteria and parasites. (Elsewhere, there were those who claimed Hurricane Katrina was God’s wrath against the morals of New Orleans). All these argue that by intervening to alleviate suffering we’re working against natural justice.
Others claim suffering is good for Tamint’s soul, as if it’s some kind of reward to die of diarrhea aged two, and we are stealing away such rewards by intervening to provide good sanitation.
And so on. Contrast all these attempts to justify suffering with the parable of the Good Samaritan. The respected priest and Levite, driven by their ideas of God and cleanliness, walk on by. They won’t get to heaven (‘Truly I tell you, whatever you did not do for one of the least of these, you did not do for me’). But the Samaritan, who is from a tribe Jesus knows full well his audience detests, “as he traveled, came where the man was; and when he saw him, he took pity on him”. The Samaritan never stops to consider whether the man’s suffering is justified, even though it was by the action of men (perhaps they thought he deserved it for his past crimes). The Samaritan is motivated not by ideology or justification, but by simple humanity, the humanity shown by any child (and he then acts with the competence of a mature adult).
Imho any theology which seeks to explain natural evil must not work against that.