One more possibility: you could take the train fo some intermediate point and spend the night. For example, you could leave Stuttgart airport at 19:18 or 20:08 and go to Frankfurt central station for 36 or 40 Euros, and then go on to Heinebach early the next morning for 20 Euros. There are many inexpensive hotels within easy walking distance from the main station in Frankfurt I know this gets you there the day after the birthday, but arriving at Stuttgart at 18:35 and leaving at 19:08 could prove to be very tight. Any delay and you're sunk.