Why are you overseeding? What is the goal? Best to resod thin spots with a sod similar to your original. Do not put a different type or lower quality of grass in the thin--or dug up--spots. Stay with sod-quality Kentucky bluegrass where it was sodded, and sow top-grade perennial rye in the back where it was hydroseeded. If your grass is already thick, not much of the seed will "take" and if it does--you will not be able to tell. Concentrate on the thin spots or anywhere soil is visible.
If you wish to improve your lawn plenty of water and a regular fertilization program (mainly slow-release) is a good bet. Naturally, you need crabgrass control, weed control, keep an eye out for insects and disease. Plan to cut with a sharp mower--twice per week.