The map does a good job of laying it out.
Since this is below that large hill/s and is spring fed, it will be hard to make into a food plot. With that much hydraulic pressure pushing the water into the low areas, it will be impossible to rearrange the land to be dry. I think your two options will look something like this: soak up as much as possible, and grow food above natural grade.
Dry it out: Black walnut, Dogwood, and maybe willows along the stream banks to act as 'batteries' to pull excess water out of the system. The higher up the hill the better if sunlight is an issue. They are not food crops, per se; but have heavy water requirements to draw off the excess. I know mature pecans require at least 50 gallons of water a day per tree. I am sure Walnuts are comparable. Also cutting the tap
root while young will force the feeder roots to do the heavy lifting for water needs, pulling that water from the surface rather than the deeper water table. You might lose some trees in a dry year; but if they are for water absorption, they would be considered sacrificial anyway. Sunflowers also are heavy drinkers. I think your
chickens might be in heaven if they could eat sunflower seeds all day. It also generates a lot of bio mass for mulching and composting beds above grade.
Above grade: Would require brining in sand mix or top soil. The water may wick up from the ground, but you have a better chance of not water logging the roots. It may take several seasons to generate
enough mass to make a difference. Otherwise it is hauling in dirt/sand.
I will give this more thought and add to the conversation after I have had time to reflect more.
Not to beat a dead horse too much, but
chickens do very well on bamboo leaves: So do cows and horses, especially as a winter forage rather than just
hay.
http://www.inbar.int/2012/03/bamboo-chicken-feed/