Line a baking sheet with parchment and the pizza crust.
Rinse and roughly chop the Swiss chard and add the leaves and ribs to a pot with 1 tablespoon of water over medium heat.
Season with 1/4 teaspoon of salt and cook until the chard is tender, about 3 minutes.
Squeeze excess water from the leaves and stems and transfer to a bowl and set aside.
Combine the tomatoes, olive oil, chili flakes, barbecue sauce and the remaining salt in a small saucepot over low to medium heat and bring to a simmer, about 10 minutes.
Meanwhile, rinse and drain the hominy in a colander over the sink.
Spread a generous layer of the sauce over the prepared pizza crust and top with hominy, Swiss chard and both cheeses.
Season the pizza with salt and pepper and bake for 15-20 minutes until cheese has melted and the sauce bubbles off the sides a bit.