Lots of advice, but not until I know more about it.

Where do you live?
What kind of grass do you have?
How much water does your sprinkler apply in 5 minutes? (my neighbor's applies 1 inch in 20 minutes. Mine applies 1 inch in 8 hours).

Don't do anything until answering the questions. Some lawns will die within 24 hours of dethatching, so your approach is possibly flawed from the start.

Also, can you post some pictures of the lawn? Take them preferably on a cloudy day or when the sun is low in the sky to avoid the harsh contrast of sun/shade. Take one from across the street looking in and take another at about 3 inches away from the blades of grass. You do not have crab grass. If you had 100% crabgrass it would be all gone by now. Crabgrass is a summer annual plant that only grows from seed every spring.

What kind of grass would you like to have? Would you like a more fine bladed grass than this 'crabgrass'?

Is there something good about having grass the same height as the sidewalk? Is that what your neighbors have? The crop circles come from using a rotary mower set too low on a bumpy soil surface. Simply raising your mowing height solves that for most grasses. For the rest you have to get into leveling the lawn. Hopefully you won't have to do that.

And did you say you wanted to reduce the thickness? I'm not sure you can promote growth and not have height and/or thickness/density.

Get ready for some different watering instructions, but I would rather know where you live and what grass you have before I launch into that.