Thanks everyone and thanks Andreas.
I thought about a raised bed, but don't mature fig tree roots run deep? I am worried that even if I plant on a mound, that the roots will ultimately end up in the saturated zone. I hate to say it, but maybe my only option is to get some of those 55 gal barrels cut in half and bury them in the ground. I won't be as great as growing straight in the ground, but it will be a heck of a lot better than growing in a 7 gal black plastic nursery pot getting baked in the sun.
At first, I wondered if it could be saltwater - I am close to the bay, but not that close. There is a small spring-fed creek that runs though my neighborhood, but I am not on the creek. I never had this problem in my previous house, but my new neighborhood is kind of country, there is no sewer drainage, everyone is on a septic tank. So maybe that is why the water doesn't get channeled away very well. I am in a flood zone X, which means I don't have to have flood insurance. I am not sure what the elevation is at my house, but the house itself sits up noticeably higher than the surrounding land. Some houses in my neighborhood are in a flood zone, but I think it is because they are on the creek.