You don't win ideological Turing tests by speculated about possible theories which you can came up with in the ivory tower. You instead need to read about the actual reasoning of the other side.

Also related: Hold Off On Proposing Solutions. In this specific situation, hold off on proposing explanations for ISIS, before you have even gathered enough information.

For example:

they destroy pre-islamic historical monuments (...) to show their supporters that they are in control and that they are serious

As far as I know, they "destroy" the monuments mostly to gain money. A small fraction of the monuments is destroyed publicly, most of them are simply stolen and sold on black market.

This doesn't make them evil masterminds, merely clever thiefs.

they cater for both the religious fanatics, and for the opportunists

Because there are not enough fanatics. Also, my connotation for "opportunist" is someone unrelated to the conflict, who sees an opportunity to make money, so they volunteer for the army. But in reality the more typical ISIS soldier is a person living on their territory, whose previous way of living was destroyed by the war, and joining ISIS is their most realistic way to avoid starvation.

Starting with misinformation and trying to invent a theory of clever masterminds, that is not the same thing as the ideological Turing test. It's more like inventing conspiracy theories for fun.

"A bunch of lunatics who kill people because they believe God told them to do it" also happens to be a short description of Old Testament. Are we going to suppose some modern-thinking evil masterminds behind that, too? Because to me it seems more like a description of humanity at its historical usual.