I know next to nutthin 'bout reading soil tests but a couple of advisories. Depending on who did the testing, some labs give recommendations for lime for agricultural purposes where they expect the lime to be mixed into the soil rather than spread on top. Keep in mind that grass does best in soil that is at a PH of 6.5ish or so.and that it is much easier to increase PH than it is to reduce it. So if you add to much lime... Second thing to keep in mind is that you do not want to add more than one pound of N per month at a time to an existing lawn. Also too much N in a seed bed is not beneficial to seedlings and can kill germenating seeds Thirdly, N and P leach pretty quickly, so adding more than the plant can use before they leach out is both a waste of money and bad for the enviorment. Maybe there are some soil test readers here, If not, I'd suggest you re-do the test with Logan Labs and pay for them to make recommendations. Just my two cents.

According to my calculations, you are short about 2 lb/k of P2O5 (phosphorus) and 4 lb/k of K2O (potassium). Probably the easiest way to get that 4 lb/k of potassium is to use a balanced NPK fertilizer, like 10-10-10 or 20-20-20. It would also give you 4 lb/k of nitrogen and 4 lb/k of phosphorus. You don't need that much phosphorus but it won't harm anything (except possibly the mycorrhizae). You want to avoid nitrogen in the summer. So if you went with the balanced fertilizer, you would be applying probably 3 applications, one a month for mid August, September, October. The 4th could be next year. Divide the NPK number into 100 to get the application rate (example, for 10-10-10, divide 10 into 100 to get 10 lb/k rate). An alternative is to find SOP, potassium sulfate, 0-0-50. You could apply that once a month, even in the summer, at 2 lb/k for four months. That would take care of the potassium. Two applications of starter fertilizer in the fall would take care of the phosphorus. Since you're planning to overseed, it would make sense to use this plan, as you could do an application of starter fertilizer at seeding and another a month later. Milorganite could substitute for the second application of starter in the fall. Use bag rate for starter or 25 lb/k of Milorganite at 5-4-0 to get 1 lb/k of phosphorus. As for nitrogen, the balanced fertilizer plan would give you 4 lb/k, which is more than you need for the year considering that you have already applied nitrogen this spring. If you use the alternative plan (which I think is better), you would get almost a lb/k with each application of starter fertilizer (1.25 with Milorganite at 25 lb/k) and then you could do a winterizer application of a quick release nitrogen in late fall after the grass has stopped growing but before the ground freezes. That would get you off to a good start next spring, when you could hold off on fertilizer until around Memorial Day. Your organic matter is low. It's good to leave clippings on the lawn when you mow. This fall mulch mow any leaves in your neighborhood that you can gather. If this is new construction, there may not be many trees but do what you can. The compost you're planning will help. Mulch mowing leaves is like making your own compost for the lawn --and you don't have to spread it! Water in your applications. Milorganite does not need to be watered in. Phosphorus tends to get tied with quickly with calcium in alkaline soil. It's there, just not available to the grass. Using organic forms of phosphorus, like Milorganite, enables a slow release of phosphorus. If you test next year and phosphorus is low, it's probably because of the alkaline soil. It's still there, just unavailable. Such is life for alkaline soil.

Wavering on replying, trying to be polite and stay on topic. I think a lot of regulars here have already read about NPK and know what a soil test is. You don't really have to reinvent the wheel, there's a balance between writing your own content and simply reading/sharing what has already been explained. Regarding the 'chemical push,' in short everything is case by case devil in the details in my view. It would depend on what soil test, what is measures, who does it, what they are recommending, have they demonstrated examples of their work, are they benefiting financially from what is happening, and so on. It's not that there is a chemical side and an anti-vaxxer side, it just actually depends on what it is. The science and scientific process is extremely important, but if you are getting so mired in the details and big words that you don't even understand what all the terms numbers and graphs mean, and it's blocking your view of just looking at the dirt, crumple the paper and bin it IMO.

FWIW, the problem with Flint water was not because they didn't have the money for water, but because of officials trying to save money and cut corners doing so. Officials denying any problem with the water for months even though they were aware of the corrosiveness of it both before and after the switch was made is what made the problem even worse. https://www.npr.org/sections/thetwo-way/2016/04/20/465545378/lead-laced-water-in-flint-a-step-by-step-look-at-the-makings-of-a-crisis There's an article to read if you want the whole story. But we're getting off topic. Rodney