I have made pita twice recently, both times it stayed puffed after baking. I know when I have bought it from the store it was flat.
It tastes great, it is just difficult to store.
Sounds like the only issue could be size. Since you've got so much more mass, you've also got that much more gluten to keep things thick and stable. Drop to about 40-50g each, get 'em nice and flat, and cook like normal with a little less total time, and you should have a proper rise and deflation. Good luck!