If the clerk says that you are not technically deemed the custodial parent, that DOES make your case tougher, but still you have the upper hand.
Elizabeth is right that the time frame is 6 months, and I would add that once you file you don't have to worry about the clock ticking. In other words, once you file for custody in your jurisdiction, the mother can not change it to her state during the course of the proceedings. So you have already beaten the clock.
Keep a journal and get any and all documentation that proves that the child has been primarily in your care for 5 years. This will give you a very strong case for custody.
Joint legal and primary custody is appropriate, but sole custody may be pushing it. I can see no justification for supervised visitation. What you consider a stunt is perfectly legal. Until a judge decrees that you are the custodial parent neither parent has any more rights than the other. The fact that you were granted CS does carry a lot of weight, but her actions were legal.
Supervised visitation is for extreme cases. It isn't easy to facilitate supervised visitation and it is very awkward for a child. It is mainly for abuse cases. If what she was doing was truly kidnapping, that may be another justification for supervised visitation, but it was not kidnapping.
Your main objective at this point is to secure a clear court order granting you custody and getting your child back. If you overkill your legal actions against her, it may backfire in your face. The judge will be looking to see how cooperative you are with the other parent.
Just get a court order that says "primary custody" granted to you. And get your child returned. Everything else is background noise that can wait until you resolve the central issue. You have the edge but don't blow it by over-reaching and getting punative. Be cooperative and reasonable or risk turning the judge against you when you need them most.