Problem with booking a BA run
 

Hi guys, I would like to book the following run
Venice (VCE) to Dallas/Fort Worth (DFW) - Sat, Aug 23
Iberia Lineas Aereas de Espana S.A. Venice (VCE) to Madrid (MAD) - Sat, Aug 23
Iberia Lineas Aereas de Espana S.A. 3249 Dep: 7:40AM Arr: 10:20AM 2h 40m Airbus A320 Business (I)
Layover in MAD 2h 10m

Iberia Lineas Aereas de Espana S.A. Madrid (MAD) to New York (JFK) - Sat, Aug 23
Iberia Lineas Aereas de Espana S.A. 6251 Dep: 12:30PM Arr: 2:45PM 8h 15m Airbus A330 Business (I)
Layover in JFK 3h 45m

American Airlines Inc. New York (JFK) to Los Angeles (LAX) - Sat, Aug 23
American Airlines Inc. 21 Dep: 6:30PM Arr: 9:45PM 6h 15m Airbus A321 (Sharklets) Business (I)
Layover in LAX 2h 30m

American Airlines Inc. Los Angeles (LAX) to Dallas/Fort Worth (DFW) - Sun, Aug 24
American Airlines Inc. 2400 Dep: 12:15AM Arr: 5:05AM 2h 50m Boeing 737 First (A)


Dallas/Fort Worth (DFW) to Venice (VCE) - Tue, Sep 2
American Airlines Inc. Dallas/Fort Worth (DFW) to Los Angeles (LAX) - Tue, Sep 2
American Airlines Inc. 2401 Dep: 6:20AM Arr: 7:35AM 3h 15m Boeing 737 First (A)
Layover in LAX 3h 25m

American Airlines Inc. Los Angeles (LAX) to New York (JFK) - Tue, Sep 2
American Airlines Inc. 12 Dep: 11:00AM Arr: 7:50PM 5h 50m Airbus A321 (Sharklets) Business (I)
Layover in JFK 3h 15m

Iberia Lineas Aereas de Espana S.A. New York (JFK) to Madrid (MAD) - Tue, Sep 2
Iberia Lineas Aereas de Espana S.A. 6258 Dep: 11:05PM Arr: 12:20PM 7h 15m Airbus A340 Business (I)
Layover in MAD Wed, Sep 3 3h 30m

Iberia Lineas Aereas de Espana S.A. Madrid (MAD) to Venice (VCE) - Wed, Sep 3
Iberia Lineas Aereas de Espana S.A. 3244 Dep: 3:50PM Arr: 6:15PM 2h 25m Airbus A321 Business (I)

it shows up 2765.50$ on ITA

However i just cannot price it right on any OTA. When I try to book it on iberia i get almost what I want except the A class flights change to economy and the whole trip rises to 6047EUR. Any tip on where and how to book it ?

I tried orbitz, kayak, expedia, vayama, hipmunk, iberia, aa.
And neither wants to cooperate with this exact fares and flights