Another thing that may help in drying out the land, if it is fairly open, is to plant some water hogging
trees that will transpire a lot of that water from down below up into the air. Willow and
bald cypress are two possibilities if you want to go this route.
And the idea of having a rice paddy could also work. Another paddy plant that would work well is
taro. Often taro is thought of as a tropical plant, but in temperate climates with winter freezes (like here in the Deep South) it will come back from the underground corms in the spring.
Learning to live with plants like these is probably going to be less effort than trying to dry out the land by digging ditches and creating better drainage.