I accidentally deposited 3.067 ETH to my self-excluded stake.com account, and live support does not let me withdraw.
I really need to withdraw my funds, what can I do?
Foremost, you should read the terms of service of Stake. Doing this will help you determine what could be done based on their policies.
As far as I know, the moment you requested to be self-excluded, you shouldn't make any transactions in that particular account because it's no longer counted as active unless the period of self-exclusion has elapsed already. Depositing funds is one of the main things you shouldn't do because you won't be allowed to withdraw it. If that's the same instance for stake, then most probably you have to wait for your self-exclusion to be over before you could get your money back.
Since you already contacted their customer support representative, it seems that that's also their policy since they didn't let you withdraw. After all, if it's already stated into the agreement, you can hardly do anything about it. If you badly need that fund, I suggest looking for an alternative way to generate that again. It's still your responsibility to double check your account before making any kind of transactions in it, so we can't really put the blame on the casino.