It isn't necessarily that low - Our 8.19 kW (solar roof) system with exactly 1/2 the capacity pointed north has a 7,876 kWh estimated annual production. In NJ, it would likely produce less. It is still definitely worth posting the layout Tesla provided, because the numbers suggest that the layout isn't ideal for production (though it could still be the optimal layout for this roof.)
If Tesla had to put some on a different roof plane you need to plug that into PVWatts separately (then add the two yourself) to get the most accurate number. Beyond that, there could be small differences in the estimates for the different types of panels, but I would guess that would not be a major difference compared to using the 300 degree roof plane in the calculations.
Hopefully they can update the layout to give you what you are looking for. There are a few reasons they might have given you the design - some better than others. On the bad reason side, they may just have been eyeballing things and didn't want to do more detailed measurements to fit more in. They may also have been prioritizing their perceived aesthetics (which I guess is more of an opinion item.)
That is what they want everyone to think, but there are multiple examples of people here that have added or subtracted panels.
If you have TOU rates, then that changes the calculations if your goal is to have the most cost-effective installation (and not necessarily the highest-producing one,) particularly since powerwalls have not been mentioned as part of your install. In your example, the west-facing panels only generate about 75% as much energy as the east-facing, but if half of that production comes when electricity is 2x the price, then you could still come out ahead. Of course, this is only an example, as it really depends on when TOU rates come in, how much higher they are, and whether you do get full net metering for the times you over-produce.
