Good point Deena. Many people do not realize that some threats of legal consequences if you are not paid money can be criminal extortion. Usually the cases are more serious. Threatening to turn someone into the police if they don't pay you money is extortion. Extortion is a crime in the United States. "Pay me $xxx, or I'll sue you until you've got nothing." - is close to extortion. "To save you the expense of litigation, we offer you the opportunity to settle the matter for the amount of $xxxx." - would not be extortion. One must be very careful with the words they use. All that being said, I don't think the threat in the OP would rise to the level of extortion, but I wanted to expand on Deena's point.
I'm astounded at your naivety that you would "made a big project" without securing your branding. If the domain name is that important to you surely you have bought it earlier?