What I currently have is grass (tough stuff) and very hard soil. Some of it is thinly graveled.

I want to replace the grass and also have something that covers the gravel. I would like something like moss that doesn't need to be mowed but having trouble finding a suitable type.

Maybe moss is not what I need. It is for Northwest Washington weather.

Whatever is used I want it to take over (choke-out) the grass on its own. I don't want to go through the drama of removing the grass. Pretty much want to sprinkle seeds.

What is it that can do that?