Their systems failed completely to prevent me from re-registering as a self-excluded player. I lost 3,240 USD on this new account. When I contacted their customer support, they refused to issue a refund, blaming me for "breaching their Terms and Conditions" by creating the new account.
Dude, you are wrong here.
You knew that somehow if you were successful with opening another account with the same details that you were going to play and then if you eventually lost that money, you would call them out and ask for a refund. Did you know that even if you won, you would have still been caught at the point when you try to withdraw the wins?
You failed to take responsibility for yourself, you broke their terms of service. I also want to assume that within this time, you also gambled on another casino where you didn't already have an account. Did you ask for a refund when you lost? I don't think so.