You are overthinking this. The Autobahn and running it fast can happen simply by planning intercity travel. First and foremost, if you plan to run a car to its limits, be sure you have rented a car that is suitable for that. If you and your son have rented a Fiat Panda and expect to push it to its limits, not good. A friend of mine rented a GT3 and drove it from Munich to Berlin. It is incomprehensible how fast he did it. Here, he is the guy whizzing past on a YZF....a bike capable of over 170mph. He has the driving skills and youthful reaction time to run at speeds, as well as a bit of a lawless flare for speed. The local police have let him know, they know he is "the one"....and suggested a more conservative coming and going.
So, rent a suitable car. Then, instead of planning an Autobahn hammer day, plan a trip that covers the Autobahn. Go somewhere. When the limits are lifted, hammer time. Go until you feel like you need to lift. If your foot is shaking because it wants you to pull up, you are getting there. Pay attention to the other cars. If you are closing on traffic, will someone pull out in front of you? Is there a faster car coming from behind you? What are the road signs telling you? Pay very close attention to the signs. Slow when you need to, go when you can. You cannot pass on the right. You had better not tailgate. In order to permit fast driving, the drivers must be very skilled and disciplined. If your plan is to go fast, you must be both.... The crashes I have seen on the Autobahn have been pretty horrible. Horrible in that no one lived. I recall being passed once by a smaller car going way too fast. Not very much later, I passed them, 4 people scattered across the highway covered up in place. Not pretty.
If your baseline is 85 mph here on a US highway, I'd be pretty careful about opening up to 120 plus....
And.....since you are planning a winter trip, you should be on winter tires....not what you want to drive hard on.