Seeking chestnut orchard groundcover seed sources

Seeking shade- and acid-soil-tolerant, very-low-growing and nitrogen-fixing groundcovers for chestnut orchard floors.

Ideally these would be low-growing enough that Autumn's fallen chestnuts could be harvested from atop them, with little mowing needed.

I've found seed of 'Empire' Birdsfoot Trefoil; Lotus corniculatus cv. 'Empire', 'Microclover' White Clover; Trifolium repens cv 'Pirouette'; Mahala Mat; Ceanothus prostratus; and Miniature Lupin; Lupinus bicolor.

I seek Black Medic; Medicago lupulina; Forest Clover; Trifolium breweri and Brewer's Lupin; Lupinus breweri, as well as Prostrate White Clover; Trifolium repens subsp. prostratum.

Seed source and other cultivar suggestions are welcome.

Brian
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I'm not sure I know of anything that fits all of those criteria, but one thing you do see a lot in temperate deciduous woodlands are bulbs, like bluebells and wild alliums. They take advantage of the early spring sun before the trees are fully leafed out, do their thing, and then go dormant when it gets shady. They're not nitrogen fixers but all that decaying foliage must contribute a bit right around the time the trees can use it.