I may have missed something, but I'm not clear about your schedule. Are you starting in Berlin, or is your first flight from Turkey to Berlin?

It appears to me that your only connection is in LHR. If so, I wouldn't hesitate to book the flight. If you miss the connection, you will be accomodated on a later flight. (On a more general point: It's more important to worry about time between flights when the last flight you book is the last flight that day.)

Slightly off-topic: AA award travel using BA is very expensive, because of BA's surcharges. Have you checked for award availability on AB (TXL-JFK or TXL-DUS-JFK) or on IB (via MAD)? AB's fees are notably lower than IB's, but both are better than BA. AB award availability can be checked at the AA website, but you would need to call to find out about IB.