1. If you want your KBG to germinate, plan on keeping the soil moist for the next three weeks. That may need watering three times a day. Note that you'll see the rye germinate in a week or so, but if you stop watering, the KBG will not germinate.

2. I've never raked the cores. They'll break up on their own.

3. The compost has a different purpose than the fertilizer. It's used to increase organic matter and soil biology and to help with moisture retention in the early stages.

4. Play sand is not the kind of sand you want. If you core aerated as heavily as you said, you can rake the cores to low spots, but the overall bumpiness should kind of even out as the cores break down.

You need to seed soon with KBG.
No rain in forecast for next 15 days in NJ
You will need to water.
I have a half acre of grass and I am spending most of my waking hours watering.
It's a pain but necessary if you want a good lawn!

There's still lots of time to think to overseed. What you don't want to do is put it down when the moisture level is low unless you are prepared to water the lawn well instead of waiting for the fall rains to bring that about.
Seeding can be done --with weather in mind--right into October. A topping of compost or good topsoil, either before or after the seeding, will help.
I firmly believe in giving lawns a topping 1/2" of compost every spring, then a topping of seed to build the turf.
Fertilizer, if not given in the fall, would then be given in the spring when the soil has warmed up. Fertilizer in spring helps fill in the bare spots.

"Seeding can be done --with weather in mind--right into October. "

That depends on an awful lot of variables. I'm technically in zone 6 (I know I say 5, but it's really 6). I seeded in October last year, but it was a dormant seeding just before our fist big snow storm, and the grass germinated this spring.

If you're seeding rye, you'd want to seed about 4 weeks before your expected first frost date. If you're seeding KBG, you'd want to seed at least 6 weeks before your expected first frost.

We don't know enough about the OP's situation to say that it's safe to seed in October for a normal fall seeding.

Thanks everyone for the responses. I am in SE PA (Lancaster County). Checking my area's estimated 1st frost timeframe looked like somewhere mid-October, so I went ahead and seeded today. With fertilizer also applied, the water sprinklers are now giving everything a good soaking.

Final question: Is it OK to mow when the original grass gets tall enough where I'd normally get the mower out or do I let it grow out of control for awhile?

I've never been to Lancaster, but I was in Philly for a while and learned how to pronounce it (after I said it with 3 syllables and all short a sounds, which resulted in much laughter among the natives).

You don't need to really soak the seed. Soaking gets water deeper into the soil, but the seeds only need water at the surface. So your best bet is to water for a little bit several times a day (maybe 5-10 minutes 3x a day).

Did you mow short before seeding? If not, you're probably going to need to let the existing grass get pretty tall. You don't want to mow until the new grass has sprouted and had a chance to set roots deep enough to withstand the vacuum created by a rotary mower.

Thanks bpgreen! Yes you hear all varieties of pronouncing Lancaster, only locals seem to get it right!

I did mow short over the weekend so it should be alright. The KBG take 3 weeks to germinate though right? The grass will be pretty high with all the watering after that long. Just try to be reasonable and let things go as long as possible?

Thanks again!

bpgreen, you say water for 5-10 minutes. Is that enough? on some postings, it says to water 15-20 minutes. I think I might start doing 10 minutes in the am and 15 when I get off work. My grass is soaked when I do the full 15 minutes or is this how it should be? I planted seeds but in areas I had to do it again due to them seeing like they floated away.

15 minutes is probably a better number in general. But different sprinklers deliver water in different amounts. Keep in mind that the goal is to keep the seeds damp (not wet). When you say soaked, that seems to be too much to me.

Good luck riggie.
Sounds like you are on your way to a better lawn!

Umm, guess I'm realizing I did a boo-boo. I laid down fertilizer right after the seed. I should have waited until they germinate! I guess I'll be dealing with a quick growing grass in the short term. How should I manage the grass length, avoid mowing at all costs? Or is it really Ok to just mulch mow when it becomes long enough?

You did fine.
Just put off mowing as long as possible and then mow at the highest setting with a newly sharpened blade and the least amount of suction.
It will be fine.

Don't know what kind of mower you have.
Hope it is not a riding mower as they produce a great deal of suction
I use a self propelled Honda and you can adjust the amount of suction you want to use!

It is a self propelled Honda. So just turn the mower down low, not full blast and take it slower in movement as to not stall/stop the mower?

By the way, I got germination today! Now 2 more weeks of agonizing watering...

If you have a lever that says bag/mulch. Put it all the way to the mulch position.
Wait until you lawn in 3 1/2-4" tall and mow one notch down from the highest setting, which is 2 3/4 "
Good luck. Keep up the watering if you don't get rain!