I got rid of my lawn a few years ago & I love not mowing. I have a gentle slope. I'm guessing that with a steep slope, you will need plants with heavy duty root systems to hold the soil & control erosion.
Instead of black plastic, I would pin in landscape fabric over the grass, then cut holes where I want the plants & dig out grass & plant. On a steep slope, you would probably have to anchor the new plant with a rock until the roots take over. In my case, we covered the landscape fabric with bark mulch.

Most plants sold as groundcovers don't have deep root systems, so they may not work in your situation. I have seen slopes planted with daylilies and siberian irises -- these seem to hold the soil.
You might google erosion control & steep slope landscaping for ideas for your area.
I think think that it's a great idea to get rid of mowing a slope.
Good luck
Susan

I've been thinking I need to make the banks of my pond easier to maintain and for my particular situation I have pretty much decided on Juniperus horizontalis (creeping juniper) I have to study how fast they grow and how close I can plant them and I know for a few years I probably will have to do clipping around them. May try mulching with all the grass clippings I get but the turkeys will be scratching in them for bugs. It doesn't work in my garden. They scratch my seedlings up. Have thought about crownvetch which is used alot along highways for erosion but I think can be messy looking.
If you have a large area, it might be easier to hit up with Roundup, then put in your plants and rocks. There are also ground covers like myrtle (vinca) and pachasandra (that is not how it is spelled but I think you know what I mean)