Double jeopardy is an interesting path. However, for double jeopardy to work, there must be a trial. Because sex offender laws are created by Ex Post Facto methods it would be very difficult to perhaps argue that viewpoint. However, I do understand where you are coming from because it does serve some validity that additional punishments or requirements are handed out long after the judicial trial phase.
I would suggest the best path is to argue Equal Protection Clause of the Fourteenth Amendment to the U.S. Constitution. I have been a long advocate of registered offenders to seek legal advice under the Rational Base test because it allows the individual to file a complaint. Under that legal test, the law must have a legitimate interest. Naturally, the state will seek the interest of public safety. The next step is that there should be a rational connection between the law means and goal. The state again would seek that additional sex offender laws reduce recidivism. Please keep in mind that I am not an attorney and not providing legal advice. I am only voicing a conversation and opinion.
The best way to remedy silly and fear-based registry laws is to use the data against the state. There are plenty of scholarly and impartial articles that demonstrate sex offender laws do more harm than good. The real issue is money is that most sex offenders are either banished from fair accessibility by specific requirements to keep them out of legislative buildings, public libraries seeking research, universities that insist that sex offenders pose a risk on campus, churches, among just a growing list of off-limits areas. It is time for the courts to be shown this data; which is non-existent. Judges need to be shown proof by impartial and convincing evidence.