I'd check with a nursery and see what plants are compatible in water for your zone. We use papyrus, water grasses, and reeds here in California. And I have papyrus in soil along the house. I have reeds in wet spots. Lookup wetland boardwalks for ideas to create a crossing for the muck and side plant it out with water plants to make a little ecosystem back there. Obviously that's not cheap, but perhaps you could use remnant materials or have a school design crew do it as a volunteer project if that's available in your area. You cannot exactly fix the swamp in the woods but maybe you can do a little something in your spot to reclaim your yard.

Easiest: sneak in a couple water tolerant trees. Like bald cypress, nyssa aquatica, whatever seems right for your zone. More difficult: some/many(?) areas have rules regarding what you can do as far as changing drainage. For example, I can not build a mound to direct drainage off my property into my neighbor's. Check your regulations and fight it! Some oaks even tolerate some water. I think Pin Oak is one. They might not reproduce naturally if submerged in the wrong seasons if I recall. Metasequoia is pretty damp tolerant if you are in zones 5, 6 or 7.... some red maples....not to the point of swimming though.

I have similar area on my property although in spots it dries out by mid-summer. I have experience with and would recommend the following plants-all are native North America: Trees (northeast/southeast portion): Acer rubrum (swamp maple)- acid to slightly acid soil Betula nigra - river birch - acid to slightly acid soil-there also a cultivar that is shrub size 'Little King' Carpinus caroliniana (american hornbeam)-neutral to slightly acid soil Querus bicolor (swamp white oak)-neutral soil Querus palustsris (pin oak) - acid soil Taxodium distichum (bald cypress)-acid soil Shrubs: aronia arbutifolia (red chokeberry) aronia melanocarpa (black chokeberry) Cephalanthus occidentalis (buttonbush) Clethra alnifolia (summersweet)-acid soil Hamamelis vernalis (vernal witchhazel)- slightly acid to acid soil Ilex glabra - (inkberry holly)-acid soil - evergreen Ilex verticliata (winterberry holly)-slightly acid to acid soil Itea virginicua (virginia sweetspire) Myrica pensylvanica (northern bayberry) Physocarpus opulifolius (common ninebark)- Viburnum tribolum -(american cranberrybush) Good Luck

That "swampy smell coming from the soil" is an indication that the growing medium is too wet. Whether you could plant the shrub outside depends on where in the world you are and how far along in development that shrub is. kimmq is kimmsr