A few thoughts - The Pizza Pilgrims pie looks like a wood fired oven (or perhaps coal or gas) bake at very high temperature and very quick. Many of us here, myself included, have battled with trying to get near this neapolitan style pizza out of a home oven. It isn't easy but with some effort you can certainly get closer to it.
Firstly my assumption is that you're cooking in a regular home oven? You're getting some underside browning, so I assume you're already using a baking stone of some type?
Your dough formula looks good, as does your mix workflow, and it looks like you're doing a good job of dough-shaping from that 3rd picture.
My initial suggestions would be:
1) in terms of dough toughness, the cold ferment in the fridge may be a factor. I stopped using the fridge a long time ago. You might want to try reducing the amount of yeast and leaving the dough at room temperature instead of the fridge.
2) I suspect you need more top-heat in your bake. There are lots of tricks to this, a few would be: preheat to get the stone as hot as possible on bake (not uncommon to preheat for 1hr or so). Then switch to the broiler element (or grill element in the UK I think) when you have the pizza in there so that the bottom is cooked by the stone, and the top is cooked by the top element. It can be tricky in some ovens to keep the thermostat from automatically turning the grill element off. Also experiment with the rack position, it may be that the upper-most position is best, but not always.
I would also check out this thread where Ryandbest has managed some excellent pies in a home oven: http://www.pizzamaking.com/forum/index.php?topic=21877.0
- they don't get much better than that out of a home oven. I'm not sure if Ryandbest is active on the forum but if so he may be willing to share some of his methods.