H_t, 1/2" steel plate stores a lot more heat than 1/8" cast iron, so you get a faster/better bake, as Don pointed out.
While there's a lot of people that are happy with 12" pizzas, once you really start taking pizza seriously, 12" is kind of pitiful. The lip on the shelf is like an inch, isn't it? If the lip does stick out that far, I might look into supporting the steel plate on steel bars instead, and extending the plate all the way to the back of the oven.
Btw, as long as the door closes, you'll be okay. You want to be touching the lip and just about touching the door. If that dimension is 14.5", get a 14.5" square stone. If it's 14.75", go with 14.75". Every fraction of an inch helps.