This probably isn't the best place to ask this, but I figured the hosta growers know more about shade than anyone.
I have an area of my lawn that only gets 2 hours of sun, if that, early morning. Probably filtered sun. It's beside the woods and in my side yard. Right now it's full of some kind of weed that sends up white/purple flowers, not sure what it is but it's nothing that creeps since there are many bare spots.

Is seeding any type of grass possible here? I'm guessing not. Do I have any option for groundcover that can be walked on, won't get a large amount of foot traffic, but won't be irritating for us to have to walk through. Something short that isn't too invasive or at least can be pulled up as it gets to where I don't want it.

If i had the choice I'd just turn it all into a shade garden, but we don't own the house so I can't make any major changes. I could probably expand the current garden out to take care of some of it, and maybe cut a garden in where it meets the woods to minimize the problem.

I am attaching a photo, it's not very good I just took it off google maps because I don't want to go outside. It shows the area in question, which is the area in the shade in the photo, which is especially bad nearest to the fence.

This is a damp area, I have a ravine in the woods there, the whole area is very shaded but that shady spot gets the most shade, grass does grow in the rest of it.

Up by the fence where the problem is, there is a wide double gate which limits what i can do to still keep the fence functional.