Hello there, congratulations on your being awarded the scholarship. I was in the same situation in that my university application deadlines were all after the award announcement as well, and since my degree has to first be evaluated by uni-assist before my first choice school will even begin to process my application I'm probably looking at mid-August acceptance at the earliest also. I am kind of nervous about it, especially since I'm leaving at the end of this month to start my language course, and have already given my job resignation notice and started saying goodbye to my friends etc, etc.
It would be really embarrassing if I moved away for two months and had to come right back (unemployed) because I didn't get accepted into a school lol. The DAAD seems to feel it's unlikely to happen so that's at least somewhat comforting then, and I'm not sure about the North American DAAD but for the region I was grouped into, I was told the award can be started as late as the spring semester of the next year so I have a bit of backup in the sense that even if I do get rejected for fall and have to come back home, two out of my three programs have spring start dates also so I can reapply and try to get in then.
I'm surprised your program (did you only apply to one?) considers GPA so heavily as well, for mine GPA is only a component of your total points for admission as they heavily weigh also the specific courses you studied in your undergraduate, regardless of the grade obtained. Did the school give you an average grade for the previous cohort that was admitted? And which city are you planning to move to in Germany, I'll be heading to Munich. Once again congratulations!