My mouth dropped open when I saw this recipe. It's basically a native american fry bread recipe!!!

I've been making this recipe all month, but I've just been frying it and cooking it on a griddle. I was getting ready to throw it onto my pizza stone next. Go figure.
Oh, so far I'm just using Gold Medal AP flour, bleached or unbleached, it just the same.
I would give this dough at least a 2 hr. room temp rest to allow the gluten to develop. It will roll and stretch beautifully (like a yeast dough) with a good oven spring.
The less you handle/stir this dough the more tender the final product.
You can knead it for a few strokes on a lightly floured surface after the room temp. rest; if you want it a bit chewier.
I would try dropping the oil to about 2T. and bring the baking powder down to 1 tsp. per cup of flour.
In general, 1 tsp baking powder is all that is required to leven a cup of flour. I have never gone over 1 1/2 tsp. per cup.
If the dough is too crumbly, the flour is probably being over measured or the liquids under measured.
Oh! The liquid (milk) should be about 100F- 105F. I haven't tried it any warmer.