Forgot to add that I am in Southern NH...Zone 5.

I would fertilize and water what you have now until late summer/early fall. If you seed now, you'll lose a lot to the heat of summer.

In late summer, buy some sod quality Kentucky Bluegrass (KBG) seed.

Once the heat breaks, you can overseed. If you like the grass you have, mow it as short as possible. If you don't like what you have, kill it with roundup.

Then core aerate or run a slit seeder. Do that in multiple directions (not just at 90 degrees or you'll get a checkerboard appearance to the new grass.

Spread the seed, then water 3x a day for about 5-10 minutes until the seed germinates (probably 3 weeks or so). Once it germinates, cut back to 1x a day for a week, then every other day for a week, then 2x a week, then 1x a week. As you decrease the frequency of watering, increase the duration. The goal is that you'll get to the point where you're watering 1x a week and putting down 1 inch of water when you do.

Thanks for your help. I'll apply the turf builder I have, and water regularly.