I know nothing about swamp oaks, so this may be way off base. That said, we had an oak in our front yard that had been dropping acorns onto the yard for years. The acorns had been ground into the soil so compactly that there was no grass there.
I didn't realize this was the problem until I was raking for a different reason and discovered acorns about 4" deep. I spent several successive days raking out acorns. When I got rid of them - Voila!! - grass!
**Take time to stop and smell the flowers
(or... as my ladybug refrigerator magnet says
"take time to stop and eat