Can God defy logic?
If God is all powerful, then yes He can defy logic, because He is more powerful than logic--He gets to decide what is and what is not logical. If, on the other hand, God cannot defy logic, that would mean that logic is more powerful than God, and therefore God's power is limited by it, and He is not all powerful.
Can God make everyone be good, without destroying individual agency?
Well, if God is all powerful then the answer is definitely yes, because if He is all powerful He can do anything, whether or not it is logical. But even if God cannot defy logic, He could still prevent us from doing evil without destroying free will. Here's why:
1) Our "free will" is already limited by God in many, many ways. We cannot do anything we want, we have innumerable constraints. Yet, these contraints aside, we still do not feel "forced" to do anything because there are still an infinite number of choices to choose from. Even if all our evil choices were taken away, we would STILL have free will because there would STILL be an infinite number of good things we can do (will I have steak or chicken or fish tonight? what TV show will I watch? etc.).
2) We want to do "good" and not do "evil". The problem is, we are not strong enough to always do good and always resist evil, and some people have difficulty realizing the difference between good and evil. If God took away our option for doing evil, we would be grateful to Him, not mad at the encroachment on our freedom (which would be minimal).
3) Some might argue that such a world would be boring and meaningless. However, if you believe God is all powerful, you must admit that He has the power to create a world that is devoid of evil but still exciting and meaningful, so that argument only holds up if God is not all powerful (God doesn't have the power to make us feel a certain way? Is He less powerful than anti-depressant medication?) Also, such an argument can also be used to say that heaven cannot exist (if heaven is devoid of evil, it is meaningless, boring, etc.).
4) One last point: by definition, there is nothing more evil than evil. Evil is as bad as it gets. So if we have to decide which is worse, "no evil" or "no free will", the obvious choice is "no evil"! Evil is much worse than a limited free will.
Now, if limited free will is considered an evil thing in its own right, then either
A)it is impossible to completely destroy evil, as destroying some evil would restrict free will and therefore create more evil. If this is true, God is not all powerful.
OR B)it is possible to completely destroy evil, since God is all powerful. Even though by our logic it is illogical to destroy evil completely, God decides what is logical in the first place--so He has the power to destroy all evil (or to have never allowed it in the first place).
If B) is true (and if we agree that evil exists), then God is not all good, because He wills evil.