I will keep up with progress and open for any suggestions. I am looking for something slightly more tender and airy but we love crunch as well. I will try a screen/grill out of the oven but usually the pizza doesn't last long enough to notice. I do like my new pizza stone alot so far. I think It seems to get hotter than my old stone. It is thicker. Looking forward to Friday to see if I can improve.
Tenderness and airiness are directly proportional to bake time. If you can't break the 6 minute bake barrier, you can kiss tender and airy goodbye. Without a good stone, this is difficult to do. You basically started off with a really thin, almost worthless stone, and with the KA purchase, you improved your oven setup a bit, but not enough. I know the last thing you want to hear is that you bought a mediocre stone, but... you bought a mediocre stone.
The only way you're going to get sub 6 minute bakes with that KA stone is to trick the oven so that it goes higher than 550. If you do a forum search for 'oven trick,' you'll see a few options, including cleaning cycle hacks and icing the thermostat. If you don't want to mess around with the oven, though, it's time to go stone shopping again. 1/2" steel plate is the reigning contender for puffy/air 4 minute NY style bakes at 550 degrees. A 16" x 16" plate should run you less than $25. For NY style, you want to get a square plate as large as your oven will fit. The larger the better.
What flour are you using? Short baking times are the critical component for airy and tender results, but the right flour helps a little also. If you're using KABF, you can bump up your volume a bit with a move to a real (bromated) pizzeria flour.