We have managed to solve the issue but you're probably not gonna like the solution
We have simply upgraded the car's firmware - all 32 (?) head units, it took us about two hours and it required skills, software and hardware belonging to a very experienced programmer (a friend of mine). It also included some moments of fear when the head unit stopped communicating but it all had a happy ending. The TV works just fine (about 15 channels here in CZ) without any additional settings.
So that might be a solution for you - either have a very experienced friend or just drive to the authorized service where they will charge something around 200 EUR I think and they should be able to upgrade the whole car's firmware to the latest version available.