It appears that they do - $450 for an antigen test, $1450 for a PCR - though how they are going to get a PCR test completed in your travel window is beyond me. For NYC you only need an antigen test. https://aeropuertosgap.com.mx/files/...22-01-21vf.pdf
Make sure they give paper copies of your result, not just a digital QR code. Heard enough reports of people getting turned away for QR codes that I personally would not risk it.

For my trips, I have done similar Section 107 - where I stay in Acapulco, Farmacias Ahorro is charging $350Mxn and if you get there in the morning it is about 20 minutes start to finish.

As a related note, if you are flying Aeromexico, they will not accept any of the in-home tests like Binax.