Indeed, there are two separate issues involved. On the one hand, the intelligent design movement seeks to remove methodological naturalism as a presupposition.
On the other hand is the intelligent design hypothesis which must stand or fall on its own merits: that certain features of the universe and life are best explained by intelligent cause rather than an undirected process such as natural selection.
The issue of motive of the supporters (on any side) is a legal sidebar. And as you have so clearly explained - whether in law, policy or education - one can speak of God and yet neither promote nor establish a religion.
In the end, the Supreme Court will clean up the mess it created with the Lemon decision.
Actually, motive is rather central. If the First Amendment were only about free speech, then the ID folks would have a free hand in government schools -- and so would everything else. But there is also the establishment clause. Free speech doesn't allow government agents to violate the establishment clause. That's why it's a necessary condition of state action that it must have a secular purpose.