Well, I've heard back from Romashuttle. They will provide a private shuttle service (airport-office-apartment & return) for € 125. Romepower.com's similar service is € 145.
On the one hand it's only a difference of € 20 - so maybe I should go with our rental agency. It might make things a bit smoother at the office.
On the other hand it is a saving of € 20 if I go with Romashuttle - € 20 which could easily be used for something else.
Since Romashuttle has a good reputation and has responded quickly to a number of questions I have had, I am going to book with them.