I forgot to mention, the tree will be in full sun!

We spent our honeymoon in Fairhope in 1979 and went back there a few years ago for our 25th anniversary. It's a beautiful little town. I live about 50 miles inland, so your winter temps are a 5-10 degrees warmer, but other than that similar climates. The back of my property is wet natured with clay soil. The most important consideration is what trees will tolerate wet feet. These include native red maple, silver maple, river birch, weeping willow, sycamore, sweet gum, sweet bay, pin oak, swamp white oak, bald cypress. You also need to consider that fast growing trees are usually weak trees that will break during a windstorm/hurricane and fall on your house. So if you must get a fast growing tree, be sure to get one that doesn't get more than 25-30 feet tall and situate it so that it at least that far from your house. My recommendation would be red or silver maple (native varieties--not the kind from up north that get 60 feet tall).

The silver maple is the trashiest tree in the list. I don't know if red maple will take standing water, but it's worth a try.

I would go with the bald cypress; it's a swamp tree to begin with and considered high quality along with oaks.

If you want an oak, I wouldn't plant a pin oak as they too are "northern" trees like the sycamore. Try a live oak again.

Try a Swamp Chestnut Oak or a Overcup Oak. I know at one time Bellingrath Gardens had these for sale in their plant shop. I bought my Swamp Chestnut Oak from MailOrderNatives a few years ago and it's already over 10ft tall.

My first thought was a Drake Elm. You can find them in the Home Depots now (just got new stock in). Great shade, medium growth, has a willowy feel as it has small leaves. I fell in love with them at the park in Foley and immediately went on a search to have that tree.
But will have to admit I liked one posters suggestion of a Bald Cypress. Beautiful tree we have them around my work place and ALWAYS have people asking about them. They do well with their feet wet. They are a decidous cypress, so don't count on it being an evergreen. But interesting leaves/fronds (unsure what you call their greenery)
And Live Oak has my vote too. They grow pretty fast when they are young and well, it's pretty much a symbol of the old South too.

I do not recommend Bald Cypress because it forms cypress "knees" (large above ground roots) as far away as 100 feet. My neighbor has one and my entire back yard is useless because of these "knees." We trip over them constantly, they ruin the lawn mower - endless problems. Now they are growing into the foundation of my home and I am very concerned about damage to my foundation. I understand a similar tree, POND Cypress, does not form the knees.