@OP,
As others said, there's nothing to hide here and signing message doesn't really need anyone's (especially cloudbet's) concerns but it should be your priority to give it immediately as it'll help you a lot in your case here and cloudbet will be proven (somehow) guilty trying to steal away your wins.
I am not sure who brainwashed OP with this thought that posting tx or signing a message using the bitcoin address is very personal. OP needs to understand that blockchain is an open ledger. A transaction can easily be traced.
Signing the message and posting the tx addresses can give OP all the advantages of proving that he really is the real owner of that account and couldbet can not keep saying their BS. There will be no question left for his ownership after that.