You forget to mention that the reason the Brits were able to install some semblance of civilization and reason among the Muslims is that the Brits were a superior military force; the Muslims were weak and unable to confront them. (Muslim pirates did have great success in fighting the British in the Mediterranean, which of course is where we came into it.)
Muslims are fine and will accept reason as long as they are afraid of us and know that we have superior force. The advent of assymetrical warfare with disproportionately powerful weapons has changed all that.
In other words, we're going to have to deal with it some other way. Bush has been trying the British approach - go to Iraq, take out the tyrant, and install a civil society that permits Muslims the freedom to get out of the clutches of their repressive and backwards religion. But, IMHO, it's not working. Conditions have changed. We have worldwide paths of communications and transportation that Muslims use only for death and destruction. The idea of creating an enclave of rationality in the midst of the irrational Muslim world, and hoping that this will spread seems to me to be virtually impossible, because the retrograde forces of Islam have used modern technology to become omnipresent and are seeking even more modern technology to have destructive power that they believe will force the entire world to submit to them.
The Israelis in Lebanon and ourselves in Iraq and to a lesser extent, in Afghanistan have demonstrated that our overwhelming superiority in Blitzkrieg warfare is greatly reduced when we undertake to occupy the very same territory we have so easily overrun. This reality coupled with a fanatical, indeed suicidal, willingness, indeed eagerness to sustain casualties means that our ability to intimidate is grossly reduced. You are quite right to point this out. I have been posting along these lines for some time.
As you said, "it's not working." I would add that if one looks at the forest instead of the trees, our situation in Iraq is counterproductive. I defined the forest to be Iran and the overall global war against Islamic fundamentalism. This is congruent with your statement in which you note, "disproportionately powerful weapons". If Iran gets the bomb it will be catastrophic for American interests everywhere. It must be the categorical aim of American foreign policy to prevent Iran getting the bomb. Our experience in Lebanon and Iraq and Afghanistan have only compromised our ability to intimidate countries like Iran and North Korea from getting the bomb.
Iraq has left us without allies, attenuated militarily, exposed as unable to cope with asymmetrical warfare in the context of an occupying army at a level of sustainable casualties, and without any good military or geopolitical options to bring to bear against Iran and, to a lesser degree, North Korea.
As you said, "The idea of creating an enclave of rationality in the midst of the irrational Muslim world, and hoping that this will spread seems to me to be virtually impossible". You say that the reason for this failure is that retrograde Islam as use modern technology to thwart it. Until one gets to the level of the bomb, I see the modern technology as a tool, or a weapon, but not an end strategy in itself. I believe Bush's noble attempt to unlock the Muslim mind with democracy is stumbling over our taxi driver.
I'm sure the ACLU is on top of this. /s