See if you can actually get a shovel into the area, or is it solid roots? You could just let the grass die and keep the area mulched. It will look neat and tidy that way. There's no law that says you have to plant anything under a tree. The tree would be perfectly happy to be undisturbed. It's a pretty tree and requires no further decoration.

If you want an evergreen shade tolerant ground cover you might try Pachysandra. I grew it under a very large conifer with very little water. Al

Thank you. I am going to look into the Pachysandra.

a ground cover of Dwarf Mondo Grass. or Acorus gramineus Ogon, or Vinca minor or Carex tumulicola.