Even though this is not a direct reply to the posted question but this topic came up in the thread. Some of you may find this information useful since there has been a somewhat recent change to the requirement to bring pets into Mexico.
https://www.aphis.usda.gov/aphis/pet-travel/by-country/pettravel-mexico
Effective 12/16/2019: A health certificate for dogs and cats is no longer needed to enter Mexico. Dogs and cats may be taken to the border without health certificate documentation, they will be inspected by SENASICA upon arrival. Please follow the guidance on this page.