Since you are using volume measurements and a brand of 00 flour that I have not used, it is hard to say with exactitude what the hydration ratio is for your formulation. However, If I measure out a cup of Caputo 00 Pizzeria flour by dipping a spoon into the flour bag to fill up the measuring cup to overflowing and then levelling off the top, I get 4.6 ounces for that cup (see, for example, Reply 5 at http://www.pizzamaking.com/forum/index.php/topic,2811.msg24540.html#msg24540
). For 3 1/2 cups, that would be 16.1 ounces. A cup of water technically weighs 8.33 ounces, but most people who measure a cup of water by eye and take note of the 1-cup marking will usually get between 8.0 and 8.2 ounces. This range places the hydration at between 50% on the low side and 51.7% on the high side. I have seen such hydration ratios for Neapolitan style doughs before but something closer to 54-55% seems to be more normal and close to the absorption rate specified for a 00 flour such as the Caputo 00 Pizzeria flour. I personally try to get as close to 60% as I can. Adding and stirring in the flour gradually and using autolyse/rest periods will usually help you get to such higher hydration ratios. In your case, unless you add some oil to your dough formulation or you are using a natural preferment and very long fermentation times, you may want to aim for around 55-57% hydration.
You didn't indicate whether you tweak the flour and/or water before you finish the dough so it is possible that my numbers are off. However, most people who measure out volumes of flour by eye will usually err on the high side (5+ ounce "cups" are quite common), resulting in even lower hydration levels. It's also possible that your brand of 00 flour weighs less than the Caputo 00 flour. I also use the Bel Aria brand of 00 flour, which is a lower protein flour, and a cup measured as described above comes to about 4.35 ounces. It is also a lower hydration flour.
I might also add that I reverse the flour/water sequence you use and add the flour to the water. I also rarely find a need to use 10 minutes of kneading, even at the Stir speed of my KitchenAid mixer. I knead just until the dough comes away from the side of the bowl and is otherwise smooth and a bit tacky. Technically, an autolyse or similar rest period is intended to shorten the overall knead time. In that context, 10 minutes of kneading seems long to me.
I'd be interested in learning of the results of your latest effort.