Hi Brock. Welcome to Permies.
I would start with making lists. Make a list of what you want to grow. Also, make a list of plants that will grow in your area that prefer or will tolerate wet feet.
Also, if you don't already know what the soil looks like, and how far down it will go until you can't dig, or until you hit a layer impermeable to water, you
should go dig a couple of holes. They needn't be big, just deep, and if you can get light
enough to see or to take a picture of the stratification of the soil, all the better. What I would check is if the water table is high enough that you get seepage out of a dug hole.
What you should probably also consider is getting a comprehensive soil test. Yes, this will only accurately measure water-soluble matter, but it can tell you important things about your soil you otherwise have to guess about.
What is the soil texture like? How much organic matter do you have in the soil? I would guess that it's probably silty, right? Lots of similarly sized fine particles, not much room for air or water to move through
root zones, maybe prone to compaction?
Do you have
wood chips available? Is there a source for mulch or organic matter to add to the soil, something like
straw, if not wood chips? Also, do you have any quantities of dead wood lying around, punky and rotting, or destined for that fate?
I ask, because
hugelkultur might be an
answer to moisture control in your case. Raised beds would get your crops up out of the wet, and buried woody matter would help maintain a steady soil humidity level. In the same vein, if there was a surplus of wood chips, I would dig deep paths around the raised beds and backfill them with wood chips. I would just dig three feet down, lay my whole logs and woody debris in rows on contour, cover those over with dirt, backfill with wood chips, and keep going until the wood chip paths were six inches above grade, and all the scraped topsoil was mounded up over the buried wood rows.
I would then inoculate with an aerated
compost extract to ensure the soil life gets a good
boost.
The wood chip paths would act as drains for excess water, would hold water in times of drought, and would act as a soil life bioreactor, benefitting the hugelbeets and everything around.
Another way you could go is by building chinampas and embracing the water-holding tendencies of your property. Chinampas are an ancient American (Aztec, I think, but from Mexico, in any case) raised
garden bed systems that were built up on lake beds to sit above the water level, wicking moisture from the lake and benefitting from the higher nutrient levels provided by the fish also raised there.
I believe traditional rice paddies work somewhat similarly, don't they? I mean, isn't it rice and clover in the paddies, and then they are flooded, killing off the clover, which release nitrogen to the rice? Fish fingerlings, carp, usually, are then raised for the season, which fertilise the paddy. It is drained seasonally, and clover is grown again with rice. Rinse and repeat.
I may have an oversimplified understanding of the traditional rice paddy system, but as that is probably what has been done there historically, using it as a basic model that you can permaculturalise might be your best idea, as opposed to trying to change the field to do something radically different.
As a last thought, are you familiar with
Fukuoka? His work might be particularly relevant in your case.
Let us know how you proceed, and good luck.
-CK
A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.
-Robert A. Heinlein