It sounds like when all that digging took place, the subsoil was brought up to the surface and as you can see, it's not very high-quality soil.
A good solution would be to first improve the soil. Do this by spreading 1-2 inches of top-quality topsoil on it. (But be home to check the delivery of topsoil first and be prepared to reject it. It should be dark, crumbly, rich soil. Too many suppliers try to call poor-quality soil topsoil.) If you can find a supplier of compost, that would be ideal to use instead of topsoil. And if you can afford to purchase large packages of sphagnum peat moss to break up and spread on top of the problem area, that would be ideal to do instead of or along with the topsoil.Till in the topsoil or other soil amendment. (You can rent a tiller for a reasonable rate.)Then it's time for reseeding. Fall is the ideal time for reseeding, but spring is also good. Stake off the area and keep it evenly moist for two or more weeks. Try to keep traffic off it for a couple of months. Be prepared to sprinkle with additional seed this fall to further thicken the grass.