The excuse of "you fucked up, your fault" is inherently dishonest when it comes to the blockchain since you will always be able to verify the fact that you were the one who sent the transaction via a signed message (save for some shitcoins).

Manual verification wouldn't even be necessary since all you would have to do is create some process that checks if a signed message (of their choice) corresponds to the sending address... and then return it to the same address. Sure, some people wouldn't have luck with interexchange transactions or third-party services but that's not the primary issue.

Unfortunately, you're looking at an exchange that literally orchestrates pump & dump schemes and I don't know if it would even be possible to hunt them down and take legal action.

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Send support tickets... though you're not likely to have much luck there: some people have had their tickets in waiting hell for years.