Deep roots aren't necessary for erosion control as long as the planting helps to cover exposed ground (both with foliage to intercept rain and with roots intertwined with their neighbors), and we don't have information on root depth range for many species. We do have a few resources for deer-resistant plants (not that anything is foolproof) and shade-tolerant species if you can cross-reference those lists for species you find appealing or suitable to the site (how damp the soil is, desired mature size, etc.):

• Groundcovers -- focused on mostly perennials and does include a couple low-growing shrubs, but won't have trees; may be suitable as filler for growing between larger-growing species
• Native Plants for Shady Slopes -- not an exhaustive list, just a few starter suggestions
• Deer Resistant Native Plants -- details not given about sunlight level or other conditions (page is in line for an update to make that selection easier)
• Landscape Plants Rated by Deer Resistance -- includes a few species we would not recommend planting, and doesn't separate species by sun/shade preferences

Miri