[CT, USA] Suggestions for Driveway Erosion Prevention

I have a long driveway and half is on a bit of a steep, awkward incline. We plan to try a retaining wall, but it's not in the budget right now. What are some native plants that I can plant on the slope to help prevent added soil from eroding, that won't damage the driveway with their roots or spreading?

The full area is part sun and our soil has a lot of clay/silt, gets moderate salt use in the winter, and has drainage but has a lot of water flowing through it off the driveway during the spring rains. We need to cover a stretch of about 30 feet. I would prefer perennials, but a reseeding annual would also be fine.