Unfortunately we don't have any research-backed plant suggestions for this situation (installing plants directly into established turf, plus contending with mowing). Having to mow over a new planting (in order to maintain the turf) would interfere with the ability of those new plants to establish. While you could cease mowing after planting, the turfgrass may still compete with the new installation enough to slow its establishment. While an arching or taller ground-covering shrub would probably eventually take over the hillside (Fragrant Sumac being one example), reversing the situation and out-competing the grass, each shrub would need to be dug into the hillside rather than sown as seed, which is not the solution you asked for. Seed is usually sown for annuals (also not the solution desired here since they don't last longer than a year) and perennials, and while a meadow-like mix of native perennial seed could be experimented with, the recommendations for meadow creation suggest that the site be cleared of competing vegetation first (as you noted).

If within your budget, you could consult with a hired Chesapeake Bay Landscape Professional, who will have training in using sustainable landscaping techniques, which should include using site conditions as-is as much as possible and selecting the right plant for those conditions without making significant (or any) alterations.

Miri