Invoking free will has always been a major part of theodicy. If God has good reason to give us the possibility to act badly, that provides us with at least a defense against the problem of evil. But to make this defense into something more like a theodicy is hard. After all, God can give us such pure characters that even though we can act badly, we are unlikely to do so.
I want to propose that we go beyond the mere alternate-possibilities part of free will in giving theodicies. The main advantage of this is that the theodicy may be capable of accomplishing more. But there is also a very nice bonus: our theodicy may then be able to appeal to compatibilists, who are (sadly, I think) a large majority of philosophers.
I think we should reflect on the ways in which one can limit a person's freedom through manipulation of the perfectly ordinary sort. Suppose Jane is much more attractive, powerful, knowledgeable and intelligent than Bob, but Jane wants Bob to freely do something. She may even want this for Bob's own sake. Nonetheless, in order not to limit Bob's freedom too much, she needs to limit the resources she uses. Even if she leaves Bob the possibility of acting otherwise, there is the ever-present danger that she is manipulating him in a way that limits his freedom.
I think the issue of manipulation is particularly pressing if what Jane wants Bob to do is to love her back. To make use of vastly greater attractiveness, power, knowledge and intelligence in order to secure the reciprocation of love is to risk being a super-stalker, someone who uses her knowledge of the secret springs of Bob's motivations in order to subtly manipulate him to love her back. Jane needs to limit what she does. She may need to make herself less attractive to Bob in order not to swamp his freedom. She may need to give him a lot of time away from herself. She might have reason not to make it be clear to him that she is doing so much for him that he cannot but love her back. These limitations are particularly plausible in the case where the love Jane seeks to have reciprocated is something like friendship or, especially, romantic love. And Scripture also presents God's love for his people as akin to marital love, in addition to being akin to parental love (presumably, God's love has no perfect analogue among human loves).
So if God wants the best kind of reciprocation of his love, perhaps he can be subtle, but not too subtle. He can make use of his knowledge of our motivations and beliefs, but not too much such knowledge. He can give us gifts, but not overload us with gifts. He may need to hide himself from us for a time. Yes, the Holy Spirit can work in the heart all the time, but the work needs to be done in a way that builds on nature if God is to achieve the best kind of reciprocation of his love.
I think there are elements of theodicy here. And a nice bonus is that they don't rely on incompatibilism.
The Incarnation is also an important element here—I am remembering Kierkegaard...