Generally, Navies are set to take the "Fastest Route" which would mean taking the Autobahn through the Alps.
You can set it to "Avoid Motorways", in which case it would still stay on Bundesstrassen but there it would select the fastest route too.
The worst choice for you would be to select "Shortest Route" as it now would guide you even over 'befahrbarer Feldweg' if that route will be shorter by even only 1 meter and will end up taking the longest time.
An additional option that can be checked is "Avoid Toll Roads" but that could make your route much longer in distance, as well as time if you drive through France, Spain, Switzerland, Austria and Italy, amongst others.
You can select to be alerted to gas stations along the route you are taking.
My preference for planing longer, multi-day trips is to keep a time in hours or distance in km in mind and then use Google maps to plan the installments for the place to which I want to go.
If you first put in start and destination, it will pick the best route for you.
Because the GPS will select a route from "current location" this little extra effort will work for you.
You now select a shorter destination that represents your intended installment and enter that in the GPS but rename it with a 01 preface. (Easily done and can be explained in detail.) You then look at the destination of the next segment but see that there is a tunnel you want to avoid.
On the Google map, select your 01 destination as the START for your next segment.
If you now see a tunnel to be avoided 300 km ahead, drag that Google route away from the tunnel. Look at that map to see the name of a city where the deviation starts and name that 02. Pick the mid point of that deviation as 03. Then select the intended end point of the segment (or a shorter one if driving time now gets too long).
The trick, when having to make multiple waypoints, is not to select a town names in Google but using right click and entering the resulting coordinates, which can be in the middle of a lane on the highway. Now, when driving to that waypoint any time that the mid point of the segment has been passed, one enters the next number for seamless driving.
Can you give us the name of any two cities for a route that may be similar of what you intend to do.