Try to go on line and have the registration paid for on line and print all pertaining info, that way you can prove that the registaration in the U.S. is paid for and waiting for you, the Mexicasn Police probably do not care to much but CBP might and or the Police on the town where the crossing is done.
I always take the plate with the tabs off and place the front one on the back, and store the back one under the front seat, I have had a plate stolen in the city of Chiuhuhua at the motel, reported it at the border crossing in El Paso.
navegator