score:7
One of the interesting things about the NJ 40470 is that it also runs as a normal international IC (nr. 60400). You will see both trains turn up in timetable searches on the SBB and DB websites. Both with exactly the same timetable. You can see the composition of that train here.
As you can see the same train carries upon departure 3 train numbers. The IC coaches in the middle are accessible with any normal domestic or international ticket or pass.
So you can indeed just get a SBB ticket for Zurich - Basel Bad Bf, and hop on this train and stay till Hamburg, using a day on your Interrail Germany pass.
The question that remains is whether you will already be able to occupy your sleeper cabin in ZΓΌrich. When this train was still operated by DB the normal sleepers were considered 2nd class, and the deluxe sleepers were 1st. The surcharge for both was the same, but you needed a 1st class ticket for the deluxe sleeper.
OBB is no longer doing that. They only publish one surcharge per accomodation class for people with passes. And the surcharge for the Deluxe sleeper is higher than for the normal one. So I suspect that class of ticket is not relevant.
So what I would do is approach the car attendant of your sleeper in ZΓΌrich and explain it to him. Ask if it is OK for you to already occupy your sleeper. If he however insist on doing this by the book just take a seat in the middle (IC) portion, and move to your sleeper at Basel Bad bf.
Also drop an email on Nightjet, and ask them...