With the U.S. still imposing trade sanctions against Iran and the current nuclear negotiations (or lack thereof) between the U.S. and Iran, I don't believe travel to Iran is a good idea for any U.S. resident. I don't know the depth of the sanctions the U.S. has imposed on Iran, but for a U.S. resident to pay for services there, could well be illegal as a U.S. resident. I do not believe U.S. residents would be very welcomed in country and would probably be a prime target for any militant group.

I expect importation of trophies taken in Iran is forbidden since the 1979 coup.