OP, the lowest fares for your trip on many websites seems to be about $1550. And this would be a multiple airline booking. And so , you have to book through a 3rd part website and not at the airline website.
For this trip, a travel agent is a much better bet. The cust service at Expedia, Orbitz or Travelocity is horrible if something goes wrong or you need to change or re-schedule . Go with a travel agent on this one.