Prairie Dropseed

The 3" - 5" base will not be enough soil for prairie dropseed, which has a very large fibrous root system. Look for a plant(s) with a rhizomatous type root (rhizome). This shallow, creeping root type is typically used for ground cover.

Assuming that your planting site will be on the dry side and in full sun, with such a shallow depth, Bearberry could work if you are looking for a single stand-alone species - as long as you are in a northerly zone. Alternatively, you could try blending several plants in groups such as Pussytoes, Labrador violet, prairie smoke, wild strawberry. All are low-growing spreaders that will tolerate dry situations.

In either case, if water runoff/erosion is a problem, consider placing some larger rocks and additional soil to create a sunny rock garden. Rocks can help slow water runoff enough to let the shallow rooted plants thrive. 

Prairie Dropseed spreads primarily by reseeding itself, but it is slow to establish and so is not an agressive spreader. Dividing plants is not necessary because this grass doesn't die-out in the center, as some grasses/sedges do. While dividing is possible, mature plants have a dense, deep fibrous root system that makes division difficult.

The seeding rate for Prairie Dropseed, for a solid stand (of a single species), is:
• 1/4 lb. per 1000 sq. ft., or
• 10 lb. per acre.

When seeding two or more grasses together, divide the seeding rate for each species by the number of species to be planted. When seeding grasses and flowers together, use one-half to two-thirds of the recommended grass seeding rate, depending upon your desired balance of flowers to grasses.