"Russ, according to Michelin, gas for that trip, in a compact car, which would really be too small for comfort on that long a trip, would be almost €40 compared to €27 for the B-W-Ticket."
That does not surprise me at all.
"But when we're on a train, we can't stop at scenic overlooks and go for a short hike or take pictures. Also, when we're in each of the towns and cities, do we hire a cab? If not, it seems we'll have just enough time to walk several blocks around the train station before rushing back to wait for/catch the next train (at least 7 trains, I would think for this trip)."
D: I share Lee's opinion on the value of train travel over car travel in Germany. But since you've decided to squeeze too much into one day, I think it's probably wisest for you to use a car. I would never choose to do it like you're doing it. It sounds like a bus tour for Asian tourists. The train not only is more relaxing for all - it civilizes your itinerary so that you dedicate a little time to the places you stop at. Having traveled by car and by train through the region, I would definitely opt for the rails and plot my destinations accordingly. With your itin, you'll have to pass up a whole lot of interesting sights and experiences to cover that much ground. But it's your trip; you've decided that zooming through is a good way to see the BF, so I'm not going to tell you not to.