Looking carefully, both Matrix and AA seem to be putting you on AA 105 LHR-JFK the arrival time is the same. They just have a different time stated for the departure.
There's a foul up somewhere.
The 10:35 departure lands at 13:45
The 15:35 departure lands at 18:15
Your second picture has you departing at 10:35 and landing at 18:15

Did you try booking on the phone by giving the agent the exact flight numbers you wanted?