Anti-West and Anti-Islam Extremists, and Free Speech

A constant comment I've heard during the whole cartoon thing, is "Yeah, I support free speech, but the cartoon is horrible". Well, you better get used to it. Free speech is now a battle-ground in the "War of Civilizations". And, whatever you believe about the necessity or existence of the "war", this battle will happen. It will happen because conservative xenophobes in the West and conservative xenophobes in the Muslim world want it to happen. And free speech is going to be used because the cost of hurting your enemy is so low.
This all has an interesting parallel with Iraq. In Iraq, extremist elements are attempting to foment civil war by blowing up the most sacred temples of the other side. This is an easy way to use a limited amount of explosives to do the most amount of damage to civil society and government: the key is that people do not remember that a violent response is exactly what the terrorists want. Similarly, the right in the West now knows that it can cause a violent response on the other side of the world merely by mocking them. Islamic fundamentalists know that they can damage the west by using this mockery as a tool of incitement. The key here, like in Iraq, is to remind citizens on both sides of the real goal of this mockery and the incited response: to cause a greater "Clash of Civilizations".
But how do you do this? The west is insecure about terrorism and its alleged decline in terms of power and prosperity in both cultural and political realms. The Islamic world is worried about its absolute power: Islam does not cover the globe as its followers want it to, and most Islamic countries are poor and corrupt.
None of us want to or will sacrifice freedom of speech. This means that the bombs are going to keep dropping. Now that politicians have tried to smooth things over, they are all going to look like a bunch of dickheads when the next bomb comes along, meaning that they will be unable to similarly smooth over any further incidents. The internet, moreover, serves as a tool for dropping bombs like no other. There is nothing more entertaining than enraging someone who takes something very seriously, and doing so without fear of reprisal. Thus whether it is wise or not to continue the dropping of lyrical bombs on the Muslim world, it is going to continue.
The key, then, is to look at the Islamic response. We need to promote less fundamentalist Islams if we are to undermine its radical version. At this point a lot of money supports radical Islam: Saudi Arabia's supports proselytizing throughout the world while their textbooks argue against interaction with Christians and Jews. Mere publicization of this fact can help, but more is needed: we need to start supporting moderate Islam.
This is tricky, however. We answer two questions:

1. How do you support moderate Islam without the use of government funds, or use government funds in a politically feasible way?
2. How do you do this without undermining moderate Islam by associating it with the west?

In economics terms: We depend on the "Marketplace of Ideas" for our own society, and want to propagate it to others as well. Our own market is creating a dangerous influence on those others because they face market intervention through suppression of free speech and official support of ideas that are harmful to the market itself. Therefore the "market of ideas" is experiencing a market failure that is threatening its overall stability. We need to intervene, but not in a way that reinforces the instability that market. How to do so?

In response to complaints that this is anti-democratic, an instance of reification of culture etc, and that what is actually happening is some failure in the subconscious of the west, I say: We face a real, practical problem, in that many millions of people want to kill us or force their religion down our throats. Most will never do this, and simply have not thought about the problem enough or cannot have access to the correct information. Here is my practical solution. What is yours? You cannot reject a proposed solution without another proposal. If we shouldn't do this, you must give an account of what we should do, in terms of actual actions.