Are you referring to 'Shakey's Pizza" when you say a "midwest Pizza" the picture you have provided looks exactly what I remember getting from Shakey's, and I loved the stuff too.
I often wondered if they used a beer component in their dough recipe, because it had a distinctive beer'ish taste to me, and the large burnt bubbles that could often be seen near the edges when it was served.
I would go after a classic Italian bread recipe, and run that through a sheeter to see what you come up with. as a younger man I would often have my face pressed up against the glass viewing window to the kitchen at Shakey's, and watch them take scaled dough balls, run them through the sheeter twice finish the stretch by hand, run a docker across the dough, top it, and get it baking. It was also common to see them popping the dough bubbles during the bake if they got too large.
I do not think you need to fold the dough over on itself to get that texture, I could see over working the dough causing your toughness issues though.
The flavor is where you want it, the large voids in the crust are where you want it, you just have a toughness issue to figure out.
Maybe try bumping up your hydration a little, scale the dough into proper weights, and roll them into balls for an overnight ferment. Hit them with a rolling pin, but do not fold it over across itself.
Or use a lower gluten content flour and then fold it over on itself. Maybe do 50% APF & 50% HGF and see what happens?
It has been years since I have done dough experiment work, so maybe what I am saying will not apply at all. I'm just thinking out loud