Had my passport stolen once, in Vietnam! Any chance I can get screwed over like this while in Iran?
Never these things happen in Iran. You won't lose your passport while in Iran anyway. I believe hotels are required to keep foreigner's passports while you are staying with them. But make a copy of your passport and visa and keep them in a separate location. If your original passport is lost, this will help speed up the process to verify your citizenship and send you on your way.
Check the cheapest Iran tours.