Under your deck, it sounds as though you have a great spot for hostas and
several other shade loving plants. Three hours of morning sun (in Asheville)
can be handled by many shade lovers, especially hostas. I have "Golden Tiara"
planted in just such a situation and it has completely filled the area in three
years.

Other suggestions include epimediums, pachysandra (there's a variety called
Alleghany Spurge), and hellebores. Dwarf mondo grass would almost look like
grass but it can take a while to fill in an area.

You might want to go over to the Botanical Garden just west of Asheville to see
what they might have growing as ground covers.

Happy planting.