i would try using less water, perhaps 1/2c less and see how that works. 3 cups of flour with 1c of water is going to land you around ~55% hydration if you measure heavy on your flour. a few years back i took my scales to my mothers and had her measure out her flour, water etc of her bread machine recipe, and i adjusted her methods and found out that there was too much oil (fat, butter) which came in at 17% and hydration was only around 50%. final recipe wound up using 3c flour and 1 1/4c water on bread flour and 1 1/3c water on high gluten flour to land hydration around ~61-64%.
try your recipe as a countertop rise, room temp, with one doughball. keep the rest in the fridge. when your counter rise dough is doubled or slightly more than doubled, try using it and see if you like the results.
in short: too much water for the AP flour, and you are probably going to want to try 3 or even 4 dough balls. bread flour will greatly help you in making dough in the pizza aspect. also, look on here for how to stretch and fold your dough, it will add a great amount of strength to your dough that kneading isn't going to provide.
also, scales are cheap. 1g increment mechanical scales are going to be more than enough to start off accurate measurements, and there is plenty of members here that use measuring spoons with great success for the salt/sugar/yeast aspect of the recipe. certain flours like specific hydration more than other flours, and some will tolerate higher amounts of water. specifically high gluten flours or lesser flours with vital wheat gluten added.