I am puzzled by the recipe you used. If you actually used one cup of cake flour and three cups of all-purpose flour, one cup of water would, by my estimation, place the hydration (the weight of water in relation to the total weight of flours) at around 46% or less (depending on the accuracy of your water measurement). That would be a fairly stiff dough, and one with a hydration considerably less than the hydration typically used for Neapolitan-style doughs. I'm guessing that the recipe does not say to use all of the all-purpose flour or it may say to add more water if necessary. I have never been able to determine what the absorption rate is for the Bel Aria flour but, if I had to guess, I would say something around 56-58%. As November noted, that is less than what you would use for stronger flours.
I happen to have some Bel Aria flour on hand so I weighed out four cups textbook style. By "textbook" style, I mean that I measured out the flour by first stirring it in the flour bag to lighten it and then lifting the flour by a tablespoon into my 1-cup measuring cup just to the point of overflowing. I then leveled off the top with a flat edge of a kitchen knife. I did not shake the measuring cup or tamp it on a hard surface. I got a total weight of 17.2 ounces. Using a hydration of 58% yields 9.976 ounces of water by weight. Volumetrically, that is equivalent to 1 cup + 3 T. + 3/8 t. I think that is the amount I would try with the Bel Aria flour (4 c.). In measuring out the water in your measuring cup, you should line up the bottom meniscus of the water with the one-cup marking, at eye level on a flat surface. Even with this careful measuring, you may find it necessary to adjust the flour and/or water. My flour may not be as fresh as yours.