I finally decided to ask the owner of the flat and the parking space whether he'd agree to having a Schuko socket installed. It's an ordinary 16A socket, giving a maximum of 3.7 kW (although Tesla's mobile charger only delivers up to 3 kW anyway, i.e. up to 13A). Housing associations can be complicated at times, but Mr B. reacted very positively and promised to ask the building manager whether an installation would be possible.
I expect the whole procedure may take a while, but that'll be another topic for the blog. And if it works out, I plan to put together a guide on the site: what you need and how to go about getting a socket like that installed.
Why is 3 kW a pretty decent option? The car sits in the garage all night, so 3 kW x 10 hours = 30 kWh, which is enough to drive about 200 km. We practically never do that many kilometres a day, so this way of charging would be completely enough for us.
If it worked out, we'd probably stop using public chargers... and then the blog might lose its point. But who knows, maybe new things to write about will turn up? 😉