Native groundcovers would probably be fine, it's just a matter of matching the species' preferences with the existing site conditions. That said, forking-in some compost may also help improve drainage at the start, and going forward, leaving leaf litter atop the planting in autumn will also help to gradually add more organic matter (as the leaf mulch breaks down in place) to further improvements to the soil texture. Soil life (worms, insects, etc.) will "till" in the amendments for you over time.

White clover is non-native, not very supportive of specialist pollinators (they only feed a few generalist pollinators), and not going to thrive (and won't flower much) in less than full sun. We can offer some other suggestions for shade-tolerant groundcovers (local natives and almost-native for species native just outside of Maryland), though whether you have issues with browsing deer may narrow that list down a bit. Using a medley of species will not only add seasonal aesthetic interest and support more wildlife, but will also boost the resilience of the planting as a whole, since different plant species have different tolerances to stress and different pest and disease vulnerabilities. Therefore, an issue that may arise in the future won't affect them all equally.

You didn't mention if you want a lawn-like substitute (that is, not very tall-growing, perhaps under a foot) or just anything that will help cover the soil, regardless of height. (Are short 2- to 3-foot shrubs okay? We'll include a couple ideas for those in that size range.)

Here are some candidates for species to help fill-in a space, but it's not an exhaustive list and there are plenty more that would serve as clumping (non-spreading) accents, especially among taller-growing perennials. Names with an * denote species that can handle more evenly-damp conditions, as the rest would appreciate halfway-decent drainage so they don't stay soggy.

• Golden Ragwort (Packera aurea)* -- evergreen
• Allegheny Spurge (Pachysandra procumbens) -- the native cousin of the oft-planted Japanese Spurge; somewhat evergreen
• Blue Wood Phlox (Phlox divaricata) and Creeping Phlox (Phlox stolonifera) -- somewhat evergreen
• Jacob's Ladder (also called Greek Valerian, despite being a local native; Polemonium reptans)
• Pussytoes (Antennaria, several species)
• Leucothoe (Leucothoe axillaris or L. fontanesiana)* -- evergreen shrub that grows wider than tall and may sucker a little (grow new stems from the roots)
• Blue Wood Aster (Symphyotrichum cordifolium, formerly Aster cordifolius) or White Wood Aster (Eurybia divaricata, formerly Aster divaricatus) -- clumping plants, but can self-seed into larger colonies to cover ground
• Foamflower (Tiarella cordifolia) -- some have been recently reclassified into several different species, so Tiarella stolonifera is the runner/spreader of the group, whereas others are more clumping; however, plant tags will still likely name all Tiarella cultivars cordifolia for now, so look for one that says it spreads via stolons
• Wild Ginger (Asarum canadense)
• Eastern / Virginia Waterleaf (Hydrophyllum virginianum) -- not as mainstream, so may be harder to find
• Partridgeberry (Mitchella repens) -- ground-hugging and slow creeper, so should be placed where it won't be smothered by faster-growing neighbors (leaf litter is fine); evergreen
• Sensitive Fern (Onoclea sensibilis)* -- spreading, and taller-growing clumpering ferns for damp sites include Cinnamon Fern (Osmundastrum/Osmunda cinnamomeum), Ostrich Fern (Matteuccia struthiopteris), and Royal Fern (Osmunda regalis)
• Summersweet (Clethra alnifolia)* -- there are dwarf forms of this shrub that only reach about 2-3 feet tall; might sucker into a wider-than-tall colony; very fragrant blooms in summer
• various Sedges (Carex, many species) -- looks like a grass, but isn't; some clump but self-seed, while some spread via runners; some are evergreen; some handle wetter soil than others
• Great Blue Lobelia (Lobelia siphilitica)* -- can self-seed

Rather than seed, which can be difficult to manage (especially if sowing in-place, where weed control will be harder), you could try planting plugs if "regular size" nursery pots are too large or costly. Plugs are young plants older than seedlings but younger than the sizes often sold at nurseries. Being cheaper and easier to plant (the root mass is much smaller), they settle-in well and catch up to older plants faster than would be expected. Native plant nurseries are stocking more plugs as they gain popularity, but sometimes certain species will still be hard to find in any form.

If you want to try seed, because many natives need a winter dormancy chilling, they might be best sown in spring or autumn (check with the seed supplier, since this will depend on how they store their seed and which species is under consideration). Sowing seed in containers first, so you can more closely monitor them for watering needs and pluck out weeds, would be simpler than sowing them in place and trying to figure out what sprouts are weeds versus desirable plants. It's not uncommon for seedlings to be hard to ID since they may not have the same foliage traits as more mature plants. Any exposed soil you can mulch in the meantime, such as with arborist wood chips. (A whole load of wood chip delivery may be too much for a small space, but some stores are selling them in smaller amounts that you could customize to what you need.)

Miri