You've definitely got a problem with your oven heat. I feel like an oven is an expensive investment so I'm reluctant to suggest buying a whole oven just to improve pizza crust, but a more capable oven helps in many ways. I prefer gas ovens and I have also highly enjoyed convection ovens.
I've found pizza stones to be effective in improving the crust of pizza.
Like you, I discovered that crust tastes much better if you can age it. Unlike you, I started my aging at room temperature and let it rise on top of the fridge where it's warm - with plastic wrap on top of the bowl. Then I might refrigerate overnight and let it rise again in a warm place before forming.
I used very high-gluten flour, because I wanted to make the crust very thin but also chewy and slightly resilient to toppings. High gluten means making it too tough was a possible problem. I compensated for the gluten in two ways: minimal work and high moisture content.
Minimal work means I didn't knead the dough at all. I used a stand mixer with a dough hook to combine the ingredients as gently as possible and as soon as the dough was even and all the flour was wet, I stopped mixing and the next time the dough got worked was when I formed the crusts. Working the dough makes the gluten form longer strands and enhances chewiness, but I wanted toughness and lightness and crispiness.
High moisture means I added much more water than the recipe suggested. I wish I could tell you how much, but every kitchen has a different effect on bread moisture so even if I gave you an exact volume of water, you'd have to adjust it. When the dough I made was mixed it was very sticky and spongy. It did not form a nice smooth dough ball. It was climbing up the sides of the mixer bowl a little bit. For minimal working, I would take the bowl off the mixer stand and cover it with plastic wrap and put it on top of the fridge to rise.
With the dough that wet, I was looking for large, weak, translucent bubbles near the top of the dough. I wouldn't punch the dough down as much as kind of pop it. Then it went into the fridge.
With the dough that wet, it wasn't easy to work it into a crust, but I could tell if I had made it right if the dough barely sprung back when stretched. I used a wooden peel that was positively caked with flour and I made the pizza right on the peel. If I put a lot of toppings on, I would shake the peel gently from time to time to make sure the crust wasn't stuck to it.
I had a gas oven that I would turn up all the way past the numbers on the dial and let it heat for more than an hour with the stone in it. When I put the pizza on the stone, a huge burst of steam would come up from the bottom of the pizza. I think you want to look for that. Cooking time should be under ten minutes if you can get the oven hot enough.
This type of dough would produce a very thin but resilient crust in the middle and would have those huge bubbles at the edges that you see in serious New York style thin crust pizza.