Combine dry ingredients in large mixing bowl and set aside.
Pour warm water into automatic bread maker pan and add dry ingredients; set machine to dough setting and turn on. Use spatula as necessary to scrape sides and incorporate evenly - dough will be soft and sticky.
Knead for only 5 minutes; remove from pan and divide into six to eight balls of dough; cover.
Using a rolling pin and board heavily covered with corn starch, very lightly stretch one dough ball into a circle about 6" in diameter and 1/4" thick. The dough will be sticky, but light hands and a generous dusting of corn starch will yield chewy and crusty (not tough) pitas.
Place on a lightly greased cookie sheet sprinkled with corn meal or GF flour. Cover cookie sheet with waxed paper to keep pitas from drying out.
Repeat rolling of each ball of dough; allow to rise in a warm place for about 30-40 minutes.
Preheat oven to 450° F; remove waxed paper and flip pitas. Bake for 3-5 minutes; remove from oven, flip pitas, and return to oven for another 3-5 minutes or until very lightly browned and just set.
Remove from oven and immediately wrap pitas in a dishtowel for 3-4 minutes.
Split along "pocket" edge of pitas with sharp knife and fill as desired. Serve immediately or store in freezer for future use.