The Weber Genesis, Spirit and Summit grills are designed to be extremely efficient in terms of BTU's used and creating an excellent grilling surface through the utilization of Flavorizer Bars. However, this causes the grill to trap most of the heat that is produced and can limit the temperatures that the Pizza Oven Box can reach.
We have done extensive testing on these and other grills the are designed to create an even and radiant cooking surface to determine the best way to improve the performance of the Pizza Oven Box on these types of grills. In most Weber gas grill models, this is obtained by simply removing the Flavorizer bars (called heat tents on other grills). This allows for more of the heat to reach into the Pizza Oven Box as the Flavorizer bars/heat tents are designed to trap the heat produced by the burners and radiate that heat to the cooking grates. You will also want to center the Pizza Oven Box from side-to-side on the cooking surface and push it all the way to the back of the cooking surface to obtain the best results.
Doing this should allow you to reach temperatures in at least the 600 F to 700 F range in 20 to 30 minutes, and cook pizza in an average of 3 to 5 minutes depending upon the style of pizza you're cooking, health of your grill (burners being in good condition), external temperatures, and wind conditions to name a few of the variables that are outside of our control. Also, on some of the older Weber Genisis models (and some other grills) the burners are so far below the cooking surface that it is difficult to generate enough heat into the Pizza Oven Box, so it can take longer to heat or may not be able to reach the desired temperatures.