I did a quick search for DUS-MIA, and the following transatlantics on 1st August might help you.

Basically DUS-MIA on Air Berlin or DUS-ORD on AA, both fairly low taxes.


01/08/2013 AB7000 DUS-MIA 09:10-13:20 (Economy), 10 hours 10 minutes
01/08/2013 AA0241 DUS-ORD 09:45-11:55 (Economy)
..AA1388 ORD-MIA 16:25-20:30 (Economy), 16 hours 45 minutes
01/08/2013 AA0241 DUS-ORD 09:45-11:55 (Economy)
..AA2378 ORD-MIA 17:45-21:50 (Economy), 18 hours 05 minutes