You will only be able to collect payment for services rendered. That means it will be until May 15th. So your damages are a total of $10,490, plus interest.
This far exceeds the small claims court limit in New Jersey, which means you would need to file the claim in superior court in New Jersey. This means that you would need to buy a form from a form website or draft your own complaint which meets the requirements in the New Jersey Rules of Civil Procedure
Then you would have to get the citation and serve the Defendant by hiring a process server.
Next, you would have to respond to any motions to dismiss which were filed against you by filing responses which contain proper legal citations and research showing why you are legally entitled to bring your suit.
Then you would conduct discovery which can be expensive and can also make or break your case.
Following discovery would be a round of summary judgment
motions to which you would have to produce evidence qualified pursuant to the New Jersey Rules of Evidence.
Assuming you make it through summary judgment, you then have to prepare your case for trial and make exhibits, and draft a jury charge for submission to the court.
Finally, you would have to try your case and prove your cause of action by a preponderance of the evidence, submitting evidence in proper format and with the correct sponsoring testimony
It's a difficult feat to attempt without a lawyer.