My guess is you could simplify the recipe, maybe make a simple flying sponge with 50 grams of flour, 50 grams of water and 5 grams of yeast and let it sit for an hour or two. I like the idea of having both white flour and whole wheat flour, I think whole wheat would add good texture and flavor to pita.
Peter Reinhart has a recipe in American Pie for carta di musica pizza crust that behaves like a pita, you bake the dough on a stone long enough for it to puff up like a pita then take it out before it starts to get brown or crisp, let it cool (it will deflate), separate it along the outside edges into two pieces, and use it as the crust for two pizzas. If one part comes out a bit too thin, he suggests baking it further and using it as crackers. I haven't tried this yet, though.
.
