Well, now we have at least two options
Imagine something is wrong with your leg. You come to a doctor and tell him about the weird pains in your leg, and how it cramps up occasionally, etc. The doctor thinks for a moment and says: Well, now we have at least two options, (1) cut off your leg, and (2) do nothing. Would you feed that was a reasonable approach to the situation?
I hope you don't think that the problem of dealing with a subversive movement is new. Ruling elites had to figure out what to do about them since time immemorial with regular successes and regular failures. There is no universal answer, never mind a simplistic one. Treating them with kid gloves has been tried (ask the Germans how well did that work with respect to the brown shirts), treating them harshly has been tried (ask the Romans how well did feeding Christians to the lions work). It's complicated.
I am not going to develop a strategy for fighting islamists here, but I strongly suspect that a successful strategy would have the following attributes:
Why do you expect trivially simple solutions to complex problems?
I expect that in order to solve any complex problem, there must be an actionable first step. Otherwise, the problem is likely to get unsolved. (Unless some solution appears randomly in the future.)
In this situation, as the first step I would probably try to establish an organization aimed at reducing islamic terrorism. Maybe just a department within some existing secret service.
Maybe it already happened.
Saying "it's difficult" may be perfectly true, but doesn't bring us any closer to solving the problem.
Trigger warning: politics is hard mode.
"How to you make America safer from terrorists" is the title of my op-ed published in Sun Sentinel, a very prominent newspaper in Florida, one of the most swingiest of the swing states in the US for the presidential election, and the one with the most votes. The maximum length of the op-ed was 450 words, and it was significantly edited by the editor, so it doesn't convey the full message I wanted with all the nuances, but such is life. My primary goal with the piece was to convey methods of thinking more rationally about politics, such as to use probabilistic thinking, evaluating the full consequences of our actions, and avoiding attention bias. I used the example of the proposal to police heavily Muslim neighborhoods as a case study. Hope this helps Floridians think more rationally and raises the sanity waterline regarding politics!
EDIT: To be totally clear, I used guesstimates for the numbers I suggested. Following Yvain/Scott Alexander's advice, I prefer to use guesstimates rather than vague statements.