Does an individual’s acknowledgement and acceptance along with failed promises to pay to another individual give the complainant a prima facia judgeme

Hello, I own a small specialized labor company providing labor for production companies in and outside of Nashville Tennessee. In May of 2018 my company preformed service for an event called Music City Jazz Fest. The promoter Marvin Spencer has yet to pay the bill of $4095 for the show call services my company provided. As I began to contact Marvin he readily acknowledged and ancceptdd the debt and made several empty promises to pay, ( all correspondaces were in emails so I have all this documented.) as time went on and I grew less and less patient, he all the sudden claimed that he did not owe this bill and he wasn’t going to pay it. Since then he has made all sorts of offers to pay a portion of the bill, which I accepted, but he failed to make any payment on the settlement and exceeded the thirty day deadline that was agreed upon. So now I’m filing a complaint and I’m pretty sure that it’s a slam dunk win for me, I have incurred loss that exceeds amount due. Am I entitled to more?