Even with flour tortilla dough, I’ve had success pressing them. I think the trick is not to over-knead because that develops the gluten. And also work in the lard by hand or with a pastry cutter, which also tamps down gluten. The tortillas I get this way aren’t super duper thin, but that’s fine by me given the ease of making them. FYI I use the bottom of a pot, not a real press.