As your planned arrival is August 28, I would suggest holding off submitting the application. I've done a number of METV via Los Angeles and their turnaround is typically 4-5 business days. The visa is in effect from the date of issuance so the closer to your date of departure the better. You can start the application, just don't submit until about 7-8 days prior to your flight and after you no longer receive messages regarding documentation.
Actually, if one does a border crossing, even intending to travel beyond the Sonoran Free Zone, a passport is not needed. However, an FFM is required, and one's date of entry is entered into an immigration database. And honestly, no matter where I've been in Mexico I've not been asked to produce a passport, and only rarely my FFM. Thankfully crossing in both directions is, to date, and despite the political nonsense afoot, has been seamless. I too am a very frequent visitor to Mexico. Once a week at the very least and for one or two months every winter.
I cross into Mexico several times a month, and spend two months every winter there. I have yet to show my passport even once. I take it with me on long duration trips but that's it. On the one or two occasions I've been stopped (traffic check, military check point, crossing), all I ever show is my driver's license, FMM and proof of auto insurance.