Here is what I would suggest:
1) Delete the NFDM to reduce the crust burning on the edges.
2) Continue managing the dough as you are, but after you sheet the dough the first time , before giving it the first 3-fold, brush some melted Crisco over 2/3 of the dough surface, then fold the dry side over onto 1/2 of the side with Crisco, then fold the final 1/3 over on top so you will now have layers of dough and fat. Let the dough rest long enough to sheet it out again and repeat with another 3-fold and Crisco addition. Allow the dough to rest again until the dough can again be sheeted. This time give the dough a 3-fold but without and fat addition, then put into the fridge to rest overnight. On the following day, remove dough from fridge, allow to temper at room temperature until the dough can be easily formed to fit your pan. Use a greased or oiled pan, allow the dough to rise in the pan for about 45-minutes (you may need to experiment to find the best time to give you exactly what you are looking for), then dress and bake.
Note: Each time the dough is sheeted it should be sheeted 90 degrees from the direction is was previously sheeted.
If the dough is sized for just a single pizza, some people like to fold the dough that last time so it just fits into the pan. Be sure to place the dough into the pan so any overlapping dough edges are placed down.
Let me know how if this gets you closed to where you want to be.
Tom Lehmann/The Dough Doctor