The Occident flour has a protein content of 12.2%. That is bread flour territory. Also, that flour is bleached and bromated.
I think you will find that most members prefer all-purpose flour for a Chicago deep-dish style. Most all-purpose flours have a protein content of around 10.5-11%, although there are some H&R (hotel and restaurant) all-purpose flours that lean toward the low side from the standpoint of protein content. A popular choice of all-purpose flour for Chicago deep-dish and cracker style pizzas is the Ceresota or Hecker's brand (they are the same flour). It has been said that those brands of flour are higher in protein content than other all-purpose flours but, based on gluten mass tests that Norma conducted on one of these flours, I am not so sure. But the Ceresota/Hecker's flours are good flours for the Chicago styles.
In your case, you could try combining the Occident flour with all-purpose flour to lower its protein content but I am afraid that you would end up with over 90% all-purpose flour. The better way to go would be to just use a good all-purpose flour. Alternatively, you might try increasing the hydration value for your recipe since the Occident flour, as essentially a bread flour, has a higher rated absorption value. I don't know if this will work, but it may be worth a try.
The Caputo 00 Pizzeria flour is not intended for the Chicago styles of pizza. Several years ago, and largely out of curiosity, I attempted some Neapolitan-inspired Chicago deep-dish pizzas using the Caputo 00 flour. The results were quite good (http://www.pizzamaking.com/forum/index.php/topic,2365.msg20625.html#msg20625
) but atypical of the classic Chicago deep-dish style. I try not to discourage anyone from trying new and different things but I think that the 00 flours are best used for the Neapolitan style and, more specifically, in the context of very high temperature ovens. In this respect, I agree with Craig, who was posting as I was composing.