NW Ohio, Zone 6a
I'm in NW Ohio in the Toledo Black-Swamp area, and the whole area is the lake bed of glacial lake erie. As such it is all FLAT FLAT FLAT!!! And its all deep heavy poorly drained clay. However, this is not terribly different from the Red River Valley of North Dakota (originally a NoDak), and the way they recondition farmland is not with trees to break up the fragipan, but with deep rooted prairie grasses! Think Sorghastrum Nutans, Big Bluestem, timothy, bermuda grass, and a number of others of similar ilk. These all have roots that go down about 10ft into the soil even in heavy clay, and will form percolation channels for the surface water to drain through. Of course the problem with this is that you then are left with incredibly tough praire-sod (the same stuff people used to build houses out of not too long ago), so good luck tilling it under! (Sub-soiling might be a better idea, but if you're not in a hurry, and you're not trying for profit then this could work too) That said the land will most likely always be a wet spot, and should be treated as such. There are many vegetable and even grain and fruit crops and a few trees too that greatly enjoy wet-yet-well-drained soil conditions. Hawthorn, Cherry, squash pumpkins and really nearly any vegetable crop will do amazingly well on heavy wet soil (so long as its not saturated, grasses in between the rows can help to greatly reduce the soil water content both by breaking up the soil and by drinking and transpiring the water). Sugar maple is good as was already mentioned, in your area Paw Paw might do alright, most of your nut trees will love the sort of heavy "bottom-land" type of soil that you have, and many can tolerate quite alot of water logging. Elderberry is fine with wet soil, some grape varieties will do okay, mushroom culture would be advantageous to introduce a lot of degraded cellulose fiber into the soil to loosen it up. Blackberries, raspberries, blueberries (if your pH is right), asparagus, walnuts, hazelnuts (although watch out for filbert blight since you're out east here), Sassafras tends to like relatively heavy wet soils, garlic grows wild out here around Toledo (Crow Garlic actually, its actually a different species but it tastes nearly the same only a bit milder and it can handle the very wet soils we have), if you like beautiful flowers marshmallow is an obvious choice, or even north american water lotus Nelumbo Americana. Then you've got plants like staghorn sumac, and prickly ash that can be sold to the ethnic foods markets around here.
Anyway there are plenty of profitable plants to be grown in relatively wet soil, but what you need to do to get it from being outright swamp to being useful, is to first (like others have said) dig a pond (preferably with an outflow or at least with some cottonwoods or cattails to evaporate the water), then trench and mound the land in ~3 to 6ft wide trenches and 10-20 foot wide high spots (can be flat doesn't need to be an actual mound, just needs to be about 1-5 ft above the water level in the trenches depending on the plants your growing). Then you can put some lotus or cattail or even wild rice and mosquito fish (or bass, crayfish, or whatnot) into the pond/trenches and pretty soon you'll have a productive and healthy ecosystem again.
