Take the larger amount of filtered water and put in the empty dough tub.
Add in the salt and stir until dissolved.
Take the initial small amount of pizza flour and combine with the water/salt. Stir until all the lumps are gone.
In a separate small bowl, dissolve the instant yeast in the small amount of water. Let it hydrate for a minute and then mix gently until it's a uniform liquid.
Combine the yeast/water mixture into the water/salt/flour mix in the dough tub. Stir well. Doing it this way may sound like a hassle, but it prevents the yeast from being too shocked by the salt mixture.
Gradually add in the larger amount of pizza flour until a dough starts to form. Be patient with this : a little at a time, making sure the dry flour is combined into the dough. It won't feel dough-like until you're about 75% through combining the flour.
At about ¾ of the way through, get your hand in there and start to combine using one hand. Hygiene first - you should have washed your hands at the start of this process of course. Wash them again before putting them in the dough.
Use your hand to pull the wet and dry parts of the dough together, scraping the edges of the bowl as you go. The motion is basically a scoop from the bottom/edges and combining into the middle, ultimately to get this as uniform as possible. If you really must then use a wooden spoon or stiff spatula.
Lightly flour a clean surface of at least 2ft x 2ft in size. Empty out the contents of the dough tub. Get your spatula in there and scrape every last piece of dough off the sides and bottom of the tub. Get any remaining wet or dry parts - you'll be kneading it all into a uniform dough. Do as much as you can to get the dough off your hand too and combine that in.
You will need to sprinkle extra flour onto the dough mass at this stage, but don't go mad as it'll change the very important hydration (water to flour) ratio for the dough. A little flour here though is both necessary and OK.
This time your hands wont get so messy. Knead the dough. Your goal is to get it all to the same consistency, kneading just for a couple of minutes or so. I like to use a motion that lightly punches a dent into the middle of the dough then fold the two sides of the dent over each other, bring in the sides and then repeat. Do what you need to do here. Keep sprinkling a little flour if you feel your hands are going to get messy.
After two or three minutes, pick up the dough and place back into what should be a fairly clean dough tub (you DID scrape all the dough out of there, right ?).
Before sealing it up, put the thermometer in the centre of the dough. It should read between 23°C and 26°C. That's 73-79°F.
Cover the dough tub, or put the lid on it. This is about hydration, so you need a good seal here with cling-film (or whatever that's called in the USA). I invested in a dough tub with a lid - that's perfect.
This needs to sit somewhere at room temperature for 24 hours. I like to keep mine on my desk in my study where its a little warmer and so I can keep an eye on it :-).