You said in part, "Our primary challenge is to figure out what tasks appeal to al Qaeda the most."
PERSONAL (NON-EXPERT) OPINION: They hate us. They want to kill us. They want to make the world one ummah under Sharia law.
As with any terrorist organization, AQ operates about the same way most terrorist organizations do. If they are prepared to attack and they have the opportunity to attack they will do so.
The good news is that our troopers and the coalition forces have scattered the heck out of the terrorists. They are very fragmented.
The bad news is that the internet and other forms of communication unites the terrorists.
Otherwise known as "sharia and sharia alike."
So let them chat.
Yup, they want to kill us all, the trick is to figure out the specifics and timing.