Steve, I would not oil the top of the dough. In the type of container you're working with, the oil, as the dough rises, will puddle along the edge. This excess oil will act like a magnet for bench flour and you'll end up with a line of flour going around the rim. In commercial settings with 100s of dough balls, cross stacking/leaving the covers off to let the dough cool is critical, but, for the home baker using single dough ball containers, it isn't necessary.
From what I can tell, there are three factors impacting your 'disappointing results:' flour, thickness factor and bake time.
Flour
All Trumps has, by it's bromated 14% nature, a very high propensity for toughness/chewiness. You can get around this by taking a few extra steps, but it isn't easy. Underkneading is critical. If you take it anywhere near smooth, with a cold ferment, you're pretty much guaranteeing toughness. At the same time, though, the dough has to be thoroughly mixed or you'll end up with wet and dry areas in the dough, resulting in major stretching problems. You want to take cold fermented AT doughs to a point where they're well mixed, but barely kneaded- a cottage cheese appearance. For me, kneading by hand, that was about 2.5 minutes total mixing/kneading time.
You can mitigate the toughness in the flour through additional oil, but once you start adding that much oil, you leave the NY style realm. Oil can also help a bit with oven spring.
Honestly, you can make AT work, with a lot of fussing, but it is far from ideal for NY style. If you can score AT, you should be able to score something with a lower protein, such as Spring King, Full Strength, King Midas Special or Occident. I wouldn't throw away the AT you've got, but, for the next bag, I'd find something with less protein.
Thickness Factor
We talked about TF in the Reinhart thread and I think you understand the direction you need to take. As you drop the TF, there's less dough in contact with the stone, less water per square inch. Since water takes a lot of energy to boil, when there's less of it, the dough will heat up faster, creating a faster reaction, providing slightly better oven spring. There are diminishing returns to this equation, so you can't just keep stretching the skin further and further, but, for NY, .075 seems to be a happy number.
Bake time
Pizza is 80% bake time. The bake time dictates the intensity of the reaction. With a faster, hotter bake, you get a more explosive reaction, producing superior oven spring. With a slower, cooler bake, the reaction is sluggish and you end up with a dense bready crumb.
Now, you can tweak the dough and, within a small margin, get slightly better or slightly worse oven spring, but you will always be anchored to your oven setup. A cordierite pizza stone is better than no pizza stone at all, but, depending on the thickness, the best bake time it's going to get you at 545 is 8 minutes, and 8 minutes, for NY, is pretty bready.
It's time to start looking for a better stone. If you're willing to deal with the weight, 1/2" steel plate, at 5:45, will give you bake times down to 3 minutes (lower than you'll need for NY).
The thickness factor should be pretty easily resolvable. With the right stone and the right flour, you should be set, but those might take a while. Until then, though, I'd increase the oil and decrease the kneading. 4% oil, is, imo pushing the boundaries of the style, but it will go a long way in giving you tenderness and should provide a more open crumb with longer bakes. Once you've got the right oven setup and flour, though, you should be able to back down from that.
