On steep slopes, we do not suggest installing by seed (a common recommendation for larger spaces). The risk of erosion in this space and losing your seed investment through rainwater washing it away is too great.
We recommend installing your native perennial flowers and/or grasses as plugs. These are small-diameter but typically deep cells that are inexpensive yet quick to establish themselves. This allows you to plant in between the existing vegetation. Plugs are often available in 24, 36 or even 72-cell trays. Local nurseries do not carry plugs, and you typically have to go directly to a grower or wholesaler. The page linked here includes a list of native plant wholesalers who sell to individuals on larger orders.
You also might want to consider using biodegradable erosion-control blankets to stabilize each unplanted, naked area until the new native plants can take over the job. The erosion-control fabric works by slowing the runoff water and allowing sediments to fall out rather than be washed away. Seeds are sown under erosion-control material and grow up through the mesh when they germinate. Live plants can be installed by cutting holes through the mesh. The roots of the plants that are growing through the erosion-control material anchor the soil to stop erosion. If you use erosion-control blankets made of biodegradable material, they will eventually disintegrate, leaving the plants to control the problem. This material is available at most nurseries. This erosion control guide includes descriptions of several other erosion control materials that may be used.