Have you considered planting on ridges? When the garden gets fit this year, till it up and spade the soil into ridges. The soil will warm faster in the spring, the seedbed will stay dryer, most likely above water at all times. You don't have to knock the ridges down every fall, but you might want to become familiar with using roundup to burn down the weeds in the spring. The key is to have a nice ridge built that will over winter without eroding down to level.
You may not want to do everything this way but the beans, tomatoes, peppers, corn would all benefit. You get the benefits of a raised bed without having to build and haul soil.
