After several failed attempts, a lot of wasted flour and shortening, and a very messy kitchen counter, I was finally able to make piaya, the ingredients and procedure I got from inq7.net December 2005 archive, which I discovered is already gone from their site. The piaya is flaky but I could not replicate the paper thinness of the store bought. They also did not puff up because they were thicker than they should be. Nevertheless I am very happy with them and ate 2 pieces, yummy.
This is exactly what was in the inq7 article:
Piaya
½ kilo flour
½ C vegetable shortening
½ kilo muscovado sugar
Mix flour and shortening, cut into 10-gm portions, flatten/press into rounds, put 10 gms muscovado, form into balls, flatten balls and bake.
Update: add a few tablespoons of water to the dough to make it more pliable.