Well.. :-) The images would have been enough.
I think I've found the problem: Time zones. To create the links properly we would need the time zone for every origin. Unfortunately the Matrix does not provide this data. I set all the dates/times to +0000 (GMT) - already thought about setting it to US eastern time. Depending on the time zone and departure time this might lead to a jump of the day, resulting in AA to mess up the flights.
I will think about a solution.. but the only "good" and final way would need another background request resolving the time zones. But I would need to create another "service" for that.