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.

They wouldn't earn any interest on them, or be able to touch them until switching the keys, but it might look good to the public, and save some customers from terrible circumstances like OP's.