So what, exactly, should moderate Muslims do?

The pope suggests that Muslims are violent.

Muslims protest by murdering a nun.

I have no doubt whatsoever that most Muslims reacted about the way I did. Killing a nun is not the solution to any problem.

Islam is plagued by not having a pope, by having every nut who was born into Islamic culture having legitimate claim to calling himself a Muslim.

But then, so does protestant Christianity. There are some lessons non-violent Islam could learn from modern Christianity, and indeed, Judiaism.

1. Force a wedge between yourself and the violent ones. Don't be confused, this is your problem, not the observers' problem. The observers see a nun being murdered by Muslims. They see silent Muslims. They draw a connection. That kind of connection is what gets us through life.
2. Drop separatist symbols. The veil in particular.
   
3. Establish women as participants of society. Your relationships at home are your own business, but when you keep women home, that's scary to the rest of us. We want to know Muslim women personally. To talk to them, to understand our shared time on earth.
4. Create a distinguishing name. The word "reform" has worked for some Jews in a vaguely analogous context, but perhaps "the religion of the crescent". Something which when we look into it, we find leadership saying "we're the peaceful, civilized ones".
5. Call the police. Nutty Christians don't get far, because even right wing Christians don't want to be associated with them. Christians call the police when they think a member of their church is out committing violent crime.