Answer: One of the most popular groundcovers for stabilizing banks is crownvetch. It grows to a height of about a foot and a half, and has pink, pea-like flowers. However, it does look a bit "weedy", dies back to the ground each fall, and can be invasive. It is, however, likely the most durable and reliable plant for covering large areas and eroded sites. Bird's foot trefoil is a similar plant.
Ajuga (carpet bugle) is another possibility. It grows only to about 4" tall with dark green or bronze-colored foliage. It, too, can be invasive.
If the area is relatively small, you might consider something like daylilies. These will spread over the years to provide good coverage, and they are quite durable. If you can add some compost to the planting holes, this may help them get established in your challenging soil.
For the shady hillside, you might try European ginger (Asarum europaeum) or bishop's hat (Epidmedium grandiflorum). It might be helpful to prune out some of the lower branches of the trees to let a little more light in.
Hope this helps you with some ideas.
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