Thanks. I will not check a bag on the inbound flight then. I'm planning to take some things home with me, so what I could do is buy a cheap piece of luggage in Germany and only check it on the return flight. With the 2:45h layover, it appears like this could work. It's 8am on a Sunday...
For the shorter connection AA-LH: It sounds like 1:50h is tight, but could work? Does the ticket in J on LH help any with that: E.g. is there an fast lane security in T1 for LH? That one is on a Friday at 9am, so should be busier.