The thing is, there is a model for how to deal with Gaza within (barely) living memory. How did we deal with Germany and Japan after the war? First of all, we beat the living crap out of them, so that messing with us again didn’t look that good, even to the hard core.
We put their leaders on trial for war crimes/crimes against humanity and after they were found guilty we hanged them. Lesser figures got lesser prison sentences. We purged their education system of Nazism/Japanese expansionism, and modeled democratic ideas.
Was it perfect? Hardly. But how much trouble have Japan and Germany given us lately?
To accomplish this, we would need to make Islam illegal.