Went back to the car rental place today and brought our saviour a bottle of champagne to thank him.
He waited for me for more than an hour in a cold empty storage place on a friday evening...
...and without his good will and patience this road trip would have been "totally different" (meaning "sucked big time").
He told me that after I left, it took him 3h30 to get to his place (which is normally around 1h15 away).
So thank you again and have one on me Mister Lux
(arrow is pointing on the champagne bottle box)
... and while I was there I asked them to recalculate our renting costs in another way (extra kilometers instead of extra day) and saved around 100€ on the final bill