GotGarlic
Chef Extraordinaire
When he was in college, he studied anthropology and concentrated on Mexico. He traveled there for research purposes and became interested in cooking. The rest is history ☺ He actually takes his employees there so they can meet Mexicans, talk with them about the food and shop in the markets.+1
If you want to make real Mexican food, Rick Bayless is the man... and he's a Chicagoan. Go figure. He's done his research. I love his videos shot in Mexico.
I think any unrefined sugar like jaggery or Muscovado would work. Most of the international grocery stores near me have both Asian and Latin American ingredients.That Chicken Tinga Tacos recipe looks good! The piloncillo may be hard to find locally in NY, but you can get it online. Light brown sugar will work as a substitute. Italian oregano is fine, too, if you can't get Mexican oregano. They are very close in flavor. If you can't get queso fresco, I would go with the mild feta. Those things are in every supermarket here, but I'm not sure about other parts of the US.
I also think queso fresco is pretty common around the country now. The huge number of Mexican and other Latin American immigrants over the decades, and their descendants, as well as the increase in the number of white Americans who like to make more authentic foods, have created a big demand for authentic ingredients. One of my cousins lives in Traverse City, MI, way up near the Upper Peninsula. She was the supervisor of a crew of Mexicans who cleaned the local mall.
Mexican oregano might still be more of a specialty item, though. I get mine from Penzeys.