Filing habeas corpus is not the writ for getting off the registry – It is the Mandamus Writ.
If you have money for the lawyer they can do it for you. If No money you can Pro Se if you know the court’s rules, or the last thing is to wait it out and see how the PSP will react to the MUNIZ – remand from the SCOTUS on Cert denial. It is a personal matter to way. . . .