After having left a couple of snarky comments on LH's Facebook page, I got several messages from frequent travellers who did exactly that - contact LH's press department. It always led to immediate compensation, no questions asked.
You can also register an account with "Vielfliegertreff", the biggest German-speaking online community for frequent travellers. LH has an official account there and will expedite claims for forum members.
I haven't found the time to do all that yet. And honestly, I find it quite sad that LH only serves those customers who know the right buttons to push. If I contact their PR department now, I'm sure I'd have my money in no time, but another poor soul waiting for months already will have to wait even longer then.
It's really sad to see how LH treats their customers, even if it is out of presumed helplessness. But contrary to what LH claims, their current service problems are not just owed to "global aviation ops problems and weather incidents". They are mostly caused by internal processes and failed management decisions.
So instead of writing to Lufthansa, I think I will take the time to inquire with Skytrax and ask them to elaborate how their perception of LH's service level can deviate so extremely from actual passenger ones.
Skytrax' detailed LH rating must sound like cynicism in the ears of passengers who recently got to experience LH's wonderful "service level". I can't imagine the other 9 airlines in the 5-star list can be too happy about that.
None are more hopelessly enslaved than those who falsely believe they are free.
(Johann Wolfgang von Goethe)