OK. This is a hugely complex issue, I know, and I have very little time and definitely no pat answers, so I'm just going to throw my twopenn'orth into the pot and hope that it contributes to the discussion, although I know it doesn't answer it.
The key factor that helps me to get my head around this (a bit!) is the factor of time. God is eternal; He is in eternity; that is to say, that God does not experience time as we do, in an ongoing sequence of 'and-then-and-then', but rather in a single eternal 'now' in which past, present and future come together.
Head's examples presuppose a before and an after: acting now to prevent a rape, or child abuse, or a war in the future. But this is to conceive of time from a human rather than an eternal perspective. For God there is no 'and-then-and-then', and so for Him, and in His creation, the before and the after, the action and its consequences, are already present.
Now, this doesn't answer, for me, the problem of evil, nor does it make it acceptable. But it does answer the question of why God doesn't intervene in specific instances to prevent harm, suffering, or abuse. Because, the way that I look at it, God creates the world free once and for all: He does not kind of watch history unfolding and go 'Oh dear, no, I don't like how that bit panned out... rewind...', because He is not watching history in a linear sequence in the way that we experience it.
It doesn't completely answer the question, I know, but it seems to me that it's important we remember that, in giving the world its freedom, God does not just cast it loose as a great seething blob of 'will' - that is, desires, appetites, self-obsession, whatever - but rather also gives us a moral direction, a sense of right and wrong, so that, at best, we not only will what is right and therefore pleasing to God (and remember that Jesus makes plain that what is pleasing to God is that we should behave well towards one another), but also act as good stewards for the world that God has given us (which means, yes, looking after the planet, but also IMO campaigning against things we believe to be wrong and seeking to change our world and make it better. So I believe that God does intervene to prevent evil, not absolutely (because the world is an imperfect world in which sin and evil patently exist) but on an individual level every single time that one of us (and I mean 'one of us human beings' not only Christians, obviously) performs an act of charity, speaks up for what we know to be right even in the face of opposition, and so on. This means that I don't look to God to intervene to make the world a better place by somehow overriding free will , but that I try to make the world a better place by using my free will for good not ill.