Try Pachysandra.

or Geranium macrorrhizum--Big Root Geranium. But kill off the stilt grass first.

I have a moss lawn ... it's evergreen and needs little weeding. I'm sorry you don't care for yours. Got deer?

Use a low groundcover, especially evergreen to cover the entire slope .... just like lawn but without mowing, and is happy in shade. What groundcover are neighbors using successfully in similar situations? I know if it was me, it would be English ivy because I know how to control it easily and it does a fantastic job of slope coverage in shade, and is healthy and trouble free.

Perhaps a ground cover juniper along the lower portion and autumn ferns on the upper half: deer won't touch either of those and it would have more visual interest than just one plant. My northern VA deer eat pachysandra and liriope so those choices are out.

your deer eat PACHYSANDRA? I won't sleep all night now.

check these out:

http://www.finegardening.com/genus/epimedium

What kind of trees are those on the slope? It makes a difference. Some trees play nicely with groundcovers and some do not. It looks to me like the trees are sucking all the fertility out of the soil with aggressive roots and you may not be able to grow much of anything under them. Or not, but at the very least, it looks like you need something to keep the soil from washing downhill and also some soil amendment and mulch. If the tree is Norway maple and the soil is dead and compacted, you aren't going to get much of anything to grow there, even the old stand bys.

Take a look at Lamium (Silver Beacon). I grow it here in Southside Virginia on the north side of my house. It is a great ground cover for the shade and it comes in several Leaf patterns. Plus it has tiny flowers bloom in the spring. Not too aggressive either.

Look up alpine gardening. Will take some trial and error with some plants but those plants like rocky hills

http://www.livetomanage.com/rock-garden-on-hill/rock-garden-on-hill-attractive-content-alpine-garden-at-wave/