From a truck-driverīs (that I am) point of view Iīd recommend routes #2 and #3 although #2 is longer than route #3 ...
Route #3 offers by far the smallest risk of delays through traffic or construction work. Stuttgart area is a nightmare around rush hour - so better avoid it. Even our Boss asks us to use the A7/A6 at daytime although that means more mileage/more truck road toll !
The only (albeit very limited) risk on my recommended routes is the A6 between "Kreuz Weinsberg" (Weinsberg interchange between A81/A6) and Bad Rappenau where road construction is underway (the A6 is gradually extended from dual to triple lane ). But the actual construction sector is just about 10mi long and in recent weeks traffic has not been obstructed too much (unless there was an accident, though ...)
Thanks for your input. I'm going to take Route #3.