I'm sure you local guy is very nice, but you don't need to do what he's recommending. When you aerate you bring seeds to the surface which have been buried for a long time. You also provide new weed-seed surfaces for any weeds which happen to blow in. Lawn guys love to do aeration because it makes their boat payments through the winter. But for what it does to and for your lawn, it is not worth it.

Secondly, crabgrass dies all by itself in the fall. Stop watering and it will die faster.

Thirdly, real lawn guys know what to get and will get it themselves. He's a handyman who doesn't really know what he's doing. When something goes wrong, he can blame you for buying the wrong stuff.

Here is the basic process. You can probably do this. The only hard part is raking up the dead grass/weeds.

1. Spray the weeds/grass with RoundUp or other product with glyphosate.
2. Continue watering daily for one week to sprout any new weed seeds that are sitting there waiting for continual soil moisture.
3. Spray again with RoundUp to kill any new weeds that sprouted.
4. Wait a couple days and rake up all the dead grass.
5. Sow new seed on that bare soil.
6. Roll it down to ensure you have good soil-to-seed contact. If the area is small enough, you can just walk on the seed to mash it into the soil.
7. Water it lightly 3x every day (breakfast, lunch, and dinner) for as long as it takes to germinate 80% of the seed. For rye it takes 2-3 weeks. For fescue it takes 3-4 weeks. For Kentucky bluegrass it takes 4-5 weeks. Water lightly means to just moisten the surface of the soil. Watering deeply wastes water and leads to other issues.
8. Mow when the new grass is 5 inches high. Mow it back to the mower's highest setting.

As the new grass is coming in, watch for thin areas where you did not get enough seed. For rye and/or fescue, this is very important, because those grasses will not spread to fill in the thin spots. Those thin spots will be full crabgrass again next August if you don't get them dense enough now. If you are planting any mix with Kentucky bluegrass in it, the KBG should fill in the thin areas and keep the crab grass out.

Many Weed "killers" (e.g. WBG etc.) recommend that 3-4 weeks pass before seeding..If you don't want to do a complete reno with RU, look into a pre=m with mesotrione (like Scotts) to reduce weed germination at seeding and apply a preM like Dimension next Spring. Aeration isn't going to be much benefit to overseeding. Look into slit-seeding/verti-cutting instead.