I am a Mexican, and I own actually a Mexican Restaurant here in Bangkok, called The Missing Burro.
What I do is simple, I ordered the meats, either the Carnitas, the Pastor, the Cochinita, the Barbacoa, and I eat all with lots of lime juice, coriander, Onion and Sauce. Then I stay at almost zero carbs while enjoying most of the delicious flavors of Mexican Food.
Tortillas are great, but can do without them most of the time!
Cheers!