The way I see it, if the West, or primarily non-Muslims, are the ones battling these extremists, we're already screwed. Now, instead of a fight between violent extremists and peaceful moderates, you have introduced elements of race and politics (it is easy, for example, for EDMD to be perceived as Western insensitivity and arrogance). Fundamentalists will find ways to exploit this marvelously.
I wouldn't draw Mohammed at all - the best thing you can do IMHO is something that targets the extremists exclusively - something moderate and liberal Muslims won't find offensive. This way you can get them behind it also - it is far easier to remove a group's credibility and relevance when a large group of "their people" are also united against it. Involving Muslims in the solution to this problem is the key - otherwise it just ends up looking like a modern day Crusade.
Edit: I mean, if they had been asked nicely I would totally agree with you. But it must be made clear that threats are not an appropriate way to deal with religious issues.
But what result are you (or Mohammed Doodlers - "MoDoods"?) hoping to achieve?
And will antagonizing militant muslims help achieve that goal?
Edit: the point is you're antagonizing waaaay more (likely on the order of 1 billion or more) than the people you're trying to, which is counter-productive.