Daylilies

One reason that the common, orange daylily ( Hemerocallis) is a good choice as a ground cover in the orchard is because the roots, while dense at the surface, are not that competitive with tree roots.  These two plants are on top of 4" by 6" cards.  As you can see it has massive roots and almost none of them penetrate deeper than six inches.

Doesn't look like much.

They don't look like much now, but they will spread by rhizomes to form a mat.  One key point is that you do NOT want improved varieties like Stella de Oro.  The improved varieties form clumps.  You want the unimproved variety that carpet the bottoms of ditches.  The unimproved variety is a triploid, has sterile seeds and spreads with abandon.

Another attribute of this plant is that it thrives in light shade.  I have seen solid colonies beneath Black Locust and Silver Maples.

A final point is that harvesters are going to walk all over these plants when picking fruit.  They will likely damage a great number of growing points.  The plants will not care.  They will fill back in in the spring.

This approach to planting between the trees is Darwinian.  I don't care if any one species or any give individual fails as long as something more useful than nettles or motherswort fills the ecological niche.