The situation is such that Coinbase is illegally holding my funds hostage and there is nothing that I can do about it.
Think of it as if you've dropped a piece of gold into a crack in the floor of a very expensive building. The owner can get it out for you, but it'll cost him a lot of money, and pose a security risk.
At the cost of some liquidity, it could be possible for them (or some other company in a similar situation) to send different litecoins back after verifying that one of their BTC addresses received the LTC - and then waiting for that "giving up" event to reclaim those LTC for themselves, covering the cost.
That would actually be quite a decent solution. They could even charge a standard fee (fixed + percentage) for this, but they'll be at risk if the exchange rate gets worse. I assume they don't want to keep a stash of any altcoin on their own.
They closed the case without replying on the 27th. I made a new enquiry on the 28th and it was closed just now without a response.
Well, they
answered your question. You can't expect a company to keep answering the same question over and over again, just because you didn't like their answer.
Now it's up to you to take further steps.