My understanding is that halacha recognizes Bais Din as having jurisdiction even on a dispute between a Jew and a gentile
It doesnt matter if halacha says this or not, There is no way the Government will accept this position. You can get every gadol to agree with you, but the DA will never agree to this and there is nothing you can do about it. And this is not a dispute between a jew and a gentile, Its a case where the government accuses a jew of breaking a law. That was not aimed specifically at jews, Everyone has to obey this same law.