I'm not sure they want to keep him at Gitmo. An "undisclosed" location, with controlled isolation where the interrogaters can start in on tinkering with his neurons, is much better. As much satisfaction as it might give to physically toture this P.O.S., his intelligence value is far too great for that. It'll take some months, but we'll doubtless put our best people on this and have him singing like a canary in the end.
Still, if it was me I certainly would be tempted to take him to Gitmo first, slap some duct tape on his mouth, and march him up and down the aisles for all the other inmates to see.