This trip isn't that complex, should be able to be found online (or maybe try ITA powertools/Bookwithmatrix), otherwise just call it in.
By the way, add another flight at the end of your trip (that you will not check in to nor fly) to lower the price. In my example the price is $711 instead of your $782, with exactly the same flights:
https://goo.gl/flights/DUcUF