I think to answer whether to use the GAI or FSIQ depends upon what the IQ score is being used for. Regardless of which you choose to use, he clearly is a very smart guy.
The GAI is a better measure of his reasoning and thinking ability by taking out his very low PSI and his very good WMI. The PSI and WMI are more associated with efficiency rather than what we often think of as true intellect. That said, deficits in these areas can impact school performance and should not be dismissed out of hand.
Given the spread between your son's scores, I am willing to bet that many evaluators would not report a FSIQ without at least mentioning the statistically significant difference between his PSI and other indices. These kind of spreads are very rare and give you important insight into his learning profile.
Did you have him tested in order to gain entrance to a gifted program? You post in the 2-E section and I wonder if he has any diagnosed learning disabilities or ADHD? Does he have any vision, visual integration or fine motor issues that may have contributed to his relatively poor performance on the PSI subtests?
When I see profiles like this, I like to compare it to a Ferrari with a very high powerful engine that is stuck in rush hour traffic. Sometimes kids with this profile have a hard time taking in new information quickly and or demonstrating their knowledge quickly and efficiently. Their intellect can be underestimated because they can't produce the output at the same rate as their peers.