Turns out having a rolling pin and actually making them thin makes the texture and flavor profoundly better.
Current process is still:
dash salt, dash oil, pinch baking powder
add water slowly until it forms a good doughy mass
knead a bit
let rest a bit
divide into two balls
flatten and cook each on the dry skillet (although I had recently fried bacon in it, so that may have affected the flavor in the direction of deliciousness) for maybe 30s per side.
They are actually flexible, chewy, and still reasonably robust. Somewhere farther up the tech tree is homemade burritos, and I am excited.