further update:
-The UK customer service was totally clueless about what to do, so they called the Italian service center who was also clueless about why the station is closing...
As prices are skyrocketing, I think I only have two options:
1. Get to the counter and see if they provide me with a taxi between the pick up point and the airport (and if not, reimburse the taxi ride)
2. Cut short the rental on the last day they are closing and rent with Hertz, and claim the difference back to Avis
In both cases I think I'll need to have some written agreement from the station.