Yellow Archangel and lemon balm will probably cover it quickly, but don't do that if you want to plant any small shrubs such as azaleas, as they will overgrow them.

There are also some grass-like plants that love moist soil
[see https://www.google.com/search?q=grass-like+plant+likes+moisture&oq=grass-like+plant+likes+moisture&aqs=chrome..69i57.19952j0j7&sourceid=chrome&es_sm=122&ie=UTF-8 ]

If you wish to have a garden, there are many plants that like moist shade; link follows. Others may have more specific ideas.

Here is a link that might be useful: Google links

Contrary to common belief, plants do not soak up excess water - they only absorb what they need to grow. Your best bet is to select plants that like moist conditions - they will not eliminate the excess water conditions but they will thrive in it........whereas most other plants would not be happy, good drainage being the watchword for 95% percent of them! With regards to OG's for this situation, both feather reed grass (Calamagrostis) and ribbon grass (Phalaris arundinacea) are extremely tolerant of wet or waterlogged soils. Be aware that ribbon grass is often considered an aggressive spreader.