Native ginger? I'm not sure about the sun. Very low growing and slowly but densely spreading.
I think the woodland phlox might be my first try.
Green and gold (Chrysogonum, I think)

I mix up with another similar one that starts with a P..? (how can I remember the one I've never grown, and forget the one I DO??) OH! Packera aurea, another possible.
Spiderwort can take sun, can grow thick clumps, most that I have are taller than 18 in bloom, then flop over and need to be cut back for summer. and can seed, (unless you cut off the seed) "Orderly and maintained' with spiderwort will be more work than these others I list.
Lyre leaf sage can also seed, a bit is much more ground-clingy except the blooming spikes. Flower on mine not very showy.
Do you have room to try 2 for a head to head competition?