My guess this is reasonably draining ground. You can test by digging a hole--look on net--fill it with water and see how long it takes to drain. A "perk" test.
I am only a novice, but what I did in an area that drained better than yours was to dig a trench, somwhat like a septic line. Mine had a pit at the end but recall that was an option. Filled it with gravel and it worked fine. Maybe today you would put landscape fabric over the gravel.
The idea that it would work came from the land I lived on. It was once owned but a brilliant deep-thinker and I found his 125 year old drains by accident. Oops. A little plugged with silt but it still worked.
Maybe in your area you could just snake a drain tile-plastic--with holes---on top of the gravel and run the water through that. Might not even need the gravel if you extend the plastic pipe.
We checked with soil and water conservation and they suggested what I did. Not very difficult and my water problem ended.
Maybe check with soil and water conservation and the local extension agent. Then I'd ask a local farmer to see if the info from the first two sounds right. Nothing beats practical application and his advice would likely ***** the first two.