Should I go back over my recent overseed with a slitseeder?

I live in zone 7A, Long Island, NY and last Sunday (9/20) I pulled the trigger and overseeded my lawn (25% or so was newly seeded areas).

[HERE](https://imgur.com/a/BsQFd2K) is where I’m at today, 9/30 on my 10th day

I had my landscapers dethatch, aerate and drop topsoil in preparation for some newly seeded areas where we removed some pachysandra and poison ivy.

Here is what I dropped via my Echo RB60 in said order:

- Jonathan Green Black Beauty Ultra

- Scott’s Starter Fertilizer w/ Tenacity

- Jonathan Green Mag-I-cal

- Jonathan Green Love Your Soil

I then rolled everything with a lawn roller which I filled about 3/4 of the way with water (ie, heavy as fuck)

At 10 days now, most areas look to be coming in nicely, but some areas look like I may have ran my sprinklers too much and washed away seed.

I did not topdress as I thought the heavy rolling would be enough, that may have been a mistake!

I’m thinking of renting an over seeder this weekend and going over everything again. I’ve used an overseeder in the past with great results and am unsure why I did not just do that again?!

As you can see form my pics linked above, some areas are thin, some have not germinated at all and some look washed away.

Here are my questions:

-Am I too late in zone 7A to seed more?

-I would be seeding on October 4th, last 5 year average soil temperatures are 60-68F until around October 20th where it starts dipping below 60F, Mid November soil temp drops to around 50F. Is this long enough for this grass seed mixture to germinate and establish itself???

-If I go over everything with an overseeder, will that rip out the short grasslings that I currently have?

-Would I have to reapply a starter fertilizer?

-Bluebird and Classen overseeder are what are available locally, is there a preference?

-No top dressing would be needed after using the overseeder, correct?

I really do not spending the $$$ to do this again as we just bought the house last fall and I would really love the grass to be as decent as possible come next spring/summer.

* Edited to add soil temps

* Edited again to add pics from today