They recently changed the law to permit nationalization of vehicles only from the year 1998, no less, no more, see Mexican law panics South Texas car dealers - Autos - MSNBC.com

My cousin used to know somebody here who was a dual Mex/USA citizen and brought a car down under a temporary import permit from California, but I am not sure as to how they went about doing that in that manner.

You can bring your car in under a tourist visa then (hopefully within 6 months) get your FM3. You don't need to get the vehicle permit updated, because it now runs with your FM3, not the dates mentioned on the permit. This part of Article 106, Article 106