"Overtake" does not really work. For best results get rid of old, rough grass.
Black Beauty is good, but there are many good seeds out there. And it contains about 10 percent "Frontier" perennial rye , (not suitable for temps over 90 degrees.)
Most seed companies change their seed ingredients from year to year, altering varieties slightly based on seed availability.
Scotts is probably the leader in seed--their tall fescue blend is a good bet. If you want professional or stadium quality, you may need to go to the online to the Seed Superstore. You want disease resistance. And a variety that can creep with rhizomes. Top seed would be wasted, though if you didn't get rid of your old junky grass.
Spray with Roundup in August and remove old sod with sod cutting machine. Apply starter fertilizer. Loosen soil and sow new seed when temps come down to about 85 in late August or early September. Rake it in so the seed is mostly buried about 1/4 inch deep. Water every day for 30 days. Then feed again to build thickness.
Simpler...and costs about the same...call a sod farm and let the professionals do the job. Call now--its going to be a busy year.