When I cook pizza on my pizza stone (at 500, electric oven, either middle or bottom rack) the dough/crust hardens too much. Say, if I pinch a corner of the pizza and lift it, the whole base will raise, as opposed to that corner, if it were softer. I cook it for 13 minutes.
I use the same dough recipe when I cook in my cast iron, same cooking details, and it ends up very soft, which I like a lot more.
edit (when I cook in my iron cast, I layer the dough with oil again, so my uneducated conclusion would be this post would be it's oil-related)
My current dough recipe is
200g flour (all purpose, will look into getting bread flour soon)
130g water, 65% hydration
1.5g yeast, 0.75%, estimated, since my food scale only measures in 2g increments
8g oil, 4%
4g salt, 2%
I mix it all in a kitchen aid mixer for 5 minutes, at varying speeds, between 1 and 4. Then I let it sit for 5 minutes, then put a thin layer of oil and put it in a sealed container in the fridge over night. Let it rise a few hours the next day before using.