The Zilker Botanical Garden in Austin has garden phlox in their plant collection and I also found a nursery in Houston that sells it. Our garden phlox collection is very mildew resistant and should be able to handle your humidity. I think it is worth a try! Be sure to plant them in a spot with good air circulation, afternoon shade and really to be certain that they get the moisture they need. The fragrant flowers will make it worth your while.
Thanks for writing!