So, I just wanted to wrap this thread up with a huge thank you to everyone, and a report of a very successful trip.
I have never, ever, in my life had such a quick experience as I did at SXF - I timed it, and from the time we landed (I'm talking wheels on the ground) to when we walked out the front door of the airport was 11 minutes.
11 MINUTES!
Got off the plane, got the bags, no line at immigration, quickly processed, and no hassle at customs, and we were out the door. Unbelievable. Had enough time to get a new SIM card and a kebab at the Ostbahnhof, and we were still sitting around for half an hour waiting for our ICE train. Very impressive performance from the German transportation infrastructure.
Having a good time at a conference as well. Thanks again for everyone's help.