Finally someone replied in the live chat (after only 10 minutes wait, Fairphone Support no longer available - #124 by Native for original post). Unfortunately the only solution offered is sending in the phone, DIY repair is not possible 
The answer to my DIY request was that the display will be replaced and some padding will be added, which is not possible to do on your own (“success of a self repair is not guaranteed”) really annoying as this means a factory reset of the phone and (according to support) 14 days without the phone… This is especially unfortunate as e.g. my banking apps require device activations via PIN letters, so quite a lot of effort…
Hopefully the repair will at least really fix the issue…