We don't know how long it would take, and if anything the experience with individual people and with other countries (including Islamic countries like Turkey) indicates that it always takes much less time than people believe. The way you cure suicidal behavior is by forcibly preventing it, which immediately breaks the self-reinforcing pattern. Once the pattern is broken, therapy can begin to try to prevent a relapse, although you have to be ready to intervene again at any moment. I see no reason to believe that it would take a hundred years; what it would take is will and dedication.
"...the condition precedent to that is total military defeat, as happened in Japan and Germany. Not a pretty picture."
Total defeat is precisely what I'm advocating as a first step—well, second step; first step is mustering the will to bring that defeat about. It certainly wouldn't be pretty, but it would be far prettier than any of the alternatives.
At any rate, I'm not saying it's guaranteed to work, just that it is incumbent upon us, as the most moral civilization in history, to try. We stand at a unique moment: We have the military might to bring about lasting reform in the Middle East, and we have both a moral and an economic imperative to do so. We can instead take any one of several short-term, utilitarian ways out, but in so doing we betray the principles this nation was founded on.