Possibly related: First leg cancelled - Etihad Airways refuse to rebook - but a different airline
I have a booking with EuroWings (booked directly on their website) to fly on 26 July from LHR (London Heathrow) to TBS (Tbilisi). Today I got an email saying that my outgoing flight has been cancelled (looks like STT to TBS leg). The email suggests I change my booking for free in "manage my booking" section on the website. Having looked on the website, there are no flights available anywhere between 10 July and 10 August.
I understand that under both UK and EU rules, I am entitled to be rebooked on a different airline if they don't have flight availability any more. For example, Lufthansa is one of their partners and they do have availability for this date.
I attempted to call their contact centre (German number only), after 20 minutes on hold I was given a different German number to call; with that number, after 30 minutes on hold, the call was simply disconnected.
Of course, I can get a full refund and book another flight, however I purchased this flight long time ago and booking another flight now would cost almost 3 times as much; considering this is for 4 people, the difference in price is nearly £2000.
What are my options for getting the rerouting I am entitled to?