Where in the United States are you? Zone 7B only tells us what plants might survive a normal winter where you are and does not include anything about what your soil conditions might be or the amount of rainfall you might expect.
The level of organic matter, at 0.27 percent is very low, but the Alfalfa you applied will, eventually, help some. Grasses, in most places, now are experiencing problems due to the heat and lack of soil moisture and will look pretty bad. Applying a synthetic fertilizer now will not really help much and may cause even more problems and it is still too hot, most places, to seed yet.
How much water has this grass gotten this past summer?

Thanks for the reply, kimmsr.

I'm in NC, close to Raleigh. Soil is mostly clay. We've had an excess of rain this year (couldn't tell you how much, exactly, but it's been a very wet year.)

Keep in mind that too much soil moisture is as bad for any plant as too little. With that low soil organic matter your clay will tend to stay too wet.

Thanks again for the reply, kimmsr. Water could be an issue, but I can't really do much about it. The soil wasn't very wet when I dug up plugs for the soil test, so I don't know.

The lawn was aerated last weekend. I put down a little more alfalfa, spread compost on the lawn and followed it with a good quality seed blend. I've ordered the fish/seaweed fertilizer from Neptune's Harvest and will apply that soon. In addition to the nitrogen, it has phosphorous, which my maple tree (in the middle of this lawn) really needs, as do the newly planted plants in an adjacent path. I'm hoping that's not a problem for my lawn, which was already high in phosphorous.

When is the best time to apply this fertilizer? Should I wait until I see germination, or apply as soon as I get it, which should be in a few days (about 5 days after dropping the seed)? I'm thinking I will apply it again a few weeks after the initial application.

Applying a fertilizer to a lawn that is stressed or is newly growing is not a good idea. Most every good resource I have seen say to wait to fertilize a new lawn until there is good, vigorous new growth or you have mowed that grass 3 times.
Clay soils, that lack adequate levels of organic matter will most often bind any plant nutrients so they are not readily available to the plants. I would spend more time and energy working on getting the level of soil organic matter up then thinking about fertilizing.

By waiting to fertilize until after 3 mowings, you are ensuring that the roots are alive and able to take up nutrients. If you use fertilizer early, there aren't any roots. But with organic fertilizer, it tends to accumulate when there are no plants to take advantage of it. By accumulate I mean the population of microbes increases. Then when the grass plants come in, the sugars released by the roots will trigger the microbes to release plant food. Then the magic happens. So I think you can apply organic fertilizer any time.

What's done is done. I think the aeration and compost was a waste of time and money which would have been better spent on soybean meal, alfalfa, Milorganite, or any other organic fert. The best bang for the buck is in fertilizer, not compost. Neptune's Harvest is a foliar spray, obviously. Your grass needs pounds and pounds of protein/nitrogen. Is there pounds and pounds of anything in that little bottle? Maybe water. That is the fundamental flaw with liquid fertilizers. Yes, it seems to green things up, but for best results you have to use it every week.

I'm concerned about why you are routinely overseeding. Do you have weeds or disease that thins out your yard? Is the yard in the shade?

What kind of grass do you have?
Is shade an issue?
What is your watering regimen (duration and frequency)?
How high/low are you mowing?
Are weeds an issue?

And can you post a picture? Best pictures are taken on a cloudy day or in the shade.

OK, so naturally, this leads me to more questions.

kimmsr, what's the best way to add organic matter? Would that be by adding compost?

dchall, I have not added any additional fertilizer since I posted. I have a bag of alfalfa and the Neptune's Harvest. From what you said, it sounds like I could put those down at any time. But, I think I'll wait a bit, just to limit walking on the seedlings, which have already begun to germinate. So in your opinion, the better way to go is to add fertilizer than compost? Is that to address my nitrogen deficit or my OM deficit, or both? (can you tell I don't understand this 100% yet?)

I overseed every fall because my lawn is fescue and in NC, that seems to be necessary. It goes dormant in the summer and weeds tend to move in. Last winter/spring, we had a chickweed invasion, and when we pulled it or it died, we were left with bald patches. We do have a good bit of shade from a large maple, which probably hogs a lot of the water, too. We mow high and water only when we haven't had rain in over a week, at a rate of about an inch per week (in one watering).

I'll try to get a picture and post it soon.

Thanks again for all the help. Despite not using chemicals for years now, I haven't been as good about the fertilizing, and having a schedule. Mostly, the lawn has received CGM for weed suppression, a couple of times a year, but that's about it. I'd love to get my soil healthy, without tilling up the lawn and starting over.

Compost will add organic matter to that soil as will mulch mowing the grass clippings back into the lawn. Using the grains, as soil food, will also add OM. Milorganite and Ringers may, but at the recommended application rates I have not seen enough OM added to warrant the expense. Mulch mowing the leaves from any deciduous trees is also a way. Where I do that the earthworms move the, now shredded, leaves into the soil in a couple of weeks so they are not noticeable.

Dchall, I noticed you are surprised by keeval and myself saying we overseed annually. But, walking around the yards near me I noticed that nearly everyone had bare spots and many have new seed put down every fall. Could it be because we have cool season fescue grass (non-spreading like KBG) that this is normal?

Also, core aeration seems like a great way to get OM and fertilizer to the roots and soil quickly. My lawn looked the best it ever has after I core aerated plus added Ringer, which conveniently fell into the holes. Why are you not a fan of core aeration?

Also, Keeval...if you have low OM you might want to start a compost pile and add shredded leaves, food scraps, and free Starbucks coffee grinds. I did this by making a 4ft by 5ft enclosure using chicken wire. Its been a year and looks great, tons of huge worms. I manually turned the pile 1x per week except when it froze and was buried by snow.

I tried just shredding directly to the lawn 2 years ago, but I guess I didn't have enough OM...it sat there for months..in the spring I ended up just re-raking it all and composting it.

The concept of over seeding a lawn annually comes from the synthetic fertilizer people because the soil a lawn fed with synthetics is so sick it will not easily support good grass growth, even though those lawns look lush and green. Once the soil a lawn grows in is made into a good healthy soil the grasses will spread on their own and over seeding will not be necessary.

Thank you all for your replies. Here's an update.

The new seed germinated and grew to about 1.5-2 inches within 2 weeks of being put down (I was amazed.) The last alfalfa application, which I put down about a week before seeding, really did green things up. I chose the Neptune's Harvest for it's phosphorous, to encourage root development, so I applied that when the shoots were about 2 inches tall.

I really hope that, now that I'm getting better about feeding the soil, I won't need to aerate every fall. I don't know whether compost should be added annually, once the soil is healthy, but that may be a subject for another post. I do know that the best my lawn ever looked, as SC77 said, was the year after I core aerated and topdressed with a lot of compost. It was so thick and looked great. I'd like to get back to that.