Its late. Just my opinion. 6 weeks before frost is best. But a shot of Speedzone would kill the weeds, (mostly). You can reseed in 7 days, 5 days is probably enough. Skip the soil amendments. Fertilize well, and again after 30 days. Overseed double rate to be sure enough will "take" to restore the green. Plan on more weed control in spring.
If you want to aerate--no need to go deep when you are trying to establish seed. One-inch deep is just fine for seed, but you need more holes, so go over it two or three times.
Apply seed before or after aerating. Seed first results in a few seeds cut in half by the tines, but more of the core soil lands on top of the seeds. Aerate and seed second results in more of the seed falling into into the bare soil in the holes. Most aeration only results in about 16 holes per sqft. Double or triple pass gives a lot more. Drag it afterwards to mix the seed and soil together.