It's too late now, but if I ran Guantanamo, I would turn it into an Islamic Studies Institute. I would hand each new internee a Qur'an in their native language (if such translation were obtainable) with parallel translation into English, and of course, parallel Arabic original text. I would assign each internee an American interrogator, with instructions to both internee and interrogator that the internee is to spend 1 hour per day instructing the interrogator in Islam, according to the internee's best understanding, and according to the Qur'an.
It may sound preposterous, but at least it would get the internees to talk. And it would provide us with a deep insight into how they understand God, Islam, the world, and themselves. We might not get the factual information we seek, but we would get to know our enemies in a profound and human way.
And they would get to know us. I would instruct the interrogators to challenge the internees' erroneous assumptions and conclusions, and I would give the interrogators plenty of backup: psychologists, theologians (of their own faith as well as Islam) philosophers, and sociologists. That way, when the internees are finally released (as most of them have been already) they would have been exposed to a different viewpoint.
Finally, it would get the US better press. Nah. That's hoping for too much.