I have not read through the whole thread but skimmed...
NJ Points do not transfer to your license, however you must understand what that means.
1. No points will be assessed to your NYS license so you will not have to pay NY any fees or will not count towards a suspension.
2. If NJ has a driver assessment fee you will be liable and if the points are sufficient your driving privileges in NJ can be suspended.
3. Although your license will have no points your infraction, if convicted, can be detected by the insurance companies and will affect your rates.
As far as lawyers in NJ go there are a few angles. Some small town courts want to negotiate before you enter the courtroom, depending on your offense. Additionally some of these towns who have smalltown lawyers that are familiar with the system and will get you the best outcome.