re: Did I misunderstand?
You need to eliminate the cultural support they are getting, never mind the physical and financial support. Much work is being done trying to convince more moderate Muslim nations to help us out.
If we can break the terror movements down to small groups operating on their own funds and without a central organizing force, I would count that as a victory. If the terror movement was devolved to just a bunch of individual Muslim Tim McVeighs, that's probably the best we can do. And getting there won't be a cakewalk.
If I had an easy answer, believe me, I'd tell you. So far, I haven't thought of anything better than what America is doing right now, and frankly, neither has anybody else to the best of my knowledge.