3. Treat Whirlwind as a network and respect the rules, in this case we will not be able to help in any way and the user would lose access to his funds assuming it's true that indeed he lost the private key
In my opinion, this is the
best only option. People should really make sure not to lose their private keys.
I agree with this last point which was mentioned in point 3. Therefore I do not agree that other people should be held responsible for mistakes they did not make and anyone who made a mistake should accept the consequences.
There is no reason to return those bitcoin to anyone claiming to have them without proof, so it should be considered a donation. If the mixer wants to return it, then he doesn't have to publicly announce, that return will potentially causing similar problems in future.