I don't think this is an answer, but its a long series of comments. TLDR; there are many more considerations to the problem of evil than you seem to address.
You've missed a key element of Leibniz's theodicy, and in a way that seems to grossly distort his thought. God creates the best of all possible worlds, yes, but this is not to say that there is some existing catalogue of possible worlds from which God chose the best one. Such an account doesn't really obviate the problem of evil; it simply denies that God is omnipotent (since he---apparently---couldn't create world without evil). Leibniz's actual view rely on a certain form of teleology: the best possible world is a world that contains suffering because (for whatever reason) it allows for a more full expression of good than would be possible in a world in which there is no suffering (thus, for example, his Discourse on Metaphysics §3). This comes quite close to what you outline as the first interpretation of Augustine's view, and is actually quite a classical argument traceable back to at least Plato and---possibly, depending on how one understands him---Heraclitus.
Incidentally, Augustinian theodicy (whether or not this qualifies as the original Christian theodicy---and I'd hesitate to assert that!) certainly depends on freedom of the will. For freedom of the will is what allows man to withdraw from God and so to create the possibility of evil. Whatever you may think of the notion of evil as the privation of good, it seems irresponsible to dismiss this view out of hand, for it ties back directly to the heart of the question: is the existence of evil (which very few deny) contrary to the existence of God? If evil is created by some means that God (for whatever reason) places beyond his control, can he be blamed for it? I don't mean to rhetorically suggest that the answer to this question is "no"; it cannot be denied, however, that it is a question that deserves consideration---for if God is blameless in the existence of evil, then no amount of evil would seem to contradict the existence of God.
Scholastic Christian thought has tended to argue that one can regard God as not being "good" in our sense without thereby asserting that God is evil, immoral, or does anything other than what is good. God's goodness is taken to be not a different goodness from our own, but more perfect, and so occasionally manifesting itself in forms that seem to us evil. God can appear to be immoral, according to human standards, but this is due to our finite inability to grasp the infinite goodness at work. This is why Aquinas and other's speak of humans as participating in the goodness of God, albeit to greater and lesser degrees of perfection; no one can attain the goodness of God, but one can approximate it. In this sense, morality isn't strictly redefined, since the same good is there for God as for humans, it is just that God is fully able to realise this good, while human beings are not.
There may be something you find unpalatable in such answers, but surely that is not sufficient to reject an argument?
Another way, perhaps with some similarities and overlap, can be found, for example, in the Bereshith Rabbah:
R. Simon said: When the Holy One, blessed be He, came to create Adam, the ministering angels formed themselves into groups and parties, some of them saying, 'Let him be created' whilst others urged, 'Let him not be created' Thus it is written, Love and Truth fought together. Righteousness and Peace combated each other (Ps. LXXXV, 11): Love said, 'Let him be created, because he will dispense acts of love'; Truth said, 'Let him not be created, because he is compounded of falsehood'; Righteousness said, 'Let him be created, because he will perform righteous deeds ; Peace said, 'Let him not be created, because he is full of strife' What did the Lord do? He took Truth and cast it to the ground. Said the ministering angels before the Holy One, blessed be He, 'Sovereign of the Universe! Why dost Thou despise Thy seal? Let Truth arise from the earth!' Hence it is written, Let truth spring up from the earth (ib. 12).
All our Rabbis say the following in the name of R. Hanina, while R. Phinehas and R. Hilkiah say it in the name of R. Simon: Me'od (E.V. 'very') is identical with Adam as it is written And God saw everything that He had made, and, behold, it was good---me'od (Gen. I, 31), i.e. and behold Adam was good. R. Huna the Elder of Sepphoris, said : While the ministering angels were arguing with each other and disputing with each other, the Holy One, blessed be He, created him. Said He to them: 'What can ye avail? Man has already been made!'
There are many ways of interpreting this text, and a great many voices at work in it. And yet, the underlying conviction through it all is that God acts according to what he sees as right, not because he has his own version of right different from another version of right, but because he can see all the various sides that created creatures cannot.
Again a similar reading can be offered of God's famous response to Job from Job 38:
Then the Lord answered Job out of the whirlwind:
“Who is this that darkens counsel by words without knowledge?
Gird up your loins like a man,
I will question you, and you shall declare to me.
“Where were you when I laid the foundation of the earth?
Tell me, if you have understanding.
Who determined its measurements—surely you know!
Or who stretched the line upon it?
On what were its bases sunk,
or who laid its cornerstone
when the morning stars sang together
and all the heavenly beings shouted for joy?
“Or who shut in the sea with doors
when it burst out from the womb?—
when I made the clouds its garment,
and thick darkness its swaddling band,
and prescribed bounds for it,
and set bars and doors,
and said, ‘Thus far shall you come, and no farther,
and here shall your proud waves be stopped’?
“Have you commanded the morning since your days began,
and caused the dawn to know its place,
so that it might take hold of the skirts of the earth,
and the wicked be shaken out of it?
It is changed like clay under the seal,
and it is dyed like a garment.
Light is withheld from the wicked,
and their uplifted arm is broken.
“Have you entered into the springs of the sea,
or walked in the recesses of the deep?
Have the gates of death been revealed to you,
or have you seen the gates of deep darkness?
Have you comprehended the expanse of the earth?
Declare, if you know all this.
“Where is the way to the dwelling of light,
and where is the place of darkness,
that you may take it to its territory
and that you may discern the paths to its home?
Surely you know, for you were born then,
and the number of your days is great!
“Have you entered the storehouses of the snow,
or have you seen the storehouses of the hail,
which I have reserved for the time of trouble,
for the day of battle and war?
What is the way to the place where the light is distributed,
or where the east wind is scattered upon the earth?
“Who has cut a channel for the torrents of rain,
and a way for the thunderbolt,
to bring rain on a land where no one lives,
on the desert, which is empty of human life,
to satisfy the waste and desolate land,
and to make the ground put forth grass?
“Has the rain a father,
or who has begotten the drops of dew?
From whose womb did the ice come forth,
and who has given birth to the hoarfrost of heaven?
The waters become hard like stone,
and the face of the deep is frozen.
“Can you bind the chains of the Pleiades,
or loose the cords of Orion?
Can you lead forth the Mazzaroth in their season,
or can you guide the Bear with its children?
Do you know the ordinances of the heavens?
Can you establish their rule on the earth?
“Can you lift up your voice to the clouds,
so that a flood of waters may cover you?
Can you send forth lightnings, so that they may go
and say to you, ‘Here we are’?
Who has put wisdom in the inward parts,
or given understanding to the mind?
Who has the wisdom to number the clouds?
Or who can tilt the waterskins of the heavens,
when the dust runs into a mass
and the clods cling together?
“Can you hunt the prey for the lion,
or satisfy the appetite of the young lions,
when they crouch in their dens,
or lie in wait in their covert?
Who provides for the raven its prey,
when its young ones cry to God,
and wander about for lack of food?
These latter two, of course, rely heavily on the inscrutable will of God, which you may not find a palatable answer. It is, nevertheless, an answer that some people have found sufficient.
More formally the problem of evil could be formulated thus (unapologetically stolen from The Stanford Encyclopedia of Philosophy):
- If God exists, then God is omnipotent, omniscient, and morally perfect.
- If God is omnipotent, then God has the power to eliminate all evil.
- If God is omniscient, then God knows when evil exists.
- If God is morally perfect, then God has the desire to eliminate all evil.
- Evil exists.
- If evil exists and God exists, then either God doesn't have the power to eliminate all evil, or doesn't know when evil exists, or doesn't have the desire to eliminate all evil.
- Therefore, God doesn't exist
It has therefore been assumed that one can resolve this problem not merely by claiming either that god is not morally perfect or not omnipotent, but that God may not be omniscient. For it would seem that if any of those three qualities is denied, the proof given above fails, and all three have been denied by various people endorsing various different doctrines.
To get at the broader question: is there a satisfactory answer to the problem of evil? For myself, I'm inclined to invoke Protagoras: "Concerning the gods, I have no means of knowing whether they exist or not, nor of what sort they may be, because of the obscurity of the subject, and the brevity of human life."