https://www.dalrymplefarm.com/

Watch the video R.L. Dalrymple is the crabgrass guru.

It comes back if you let it reseed. Slight renovation helps each year. 3-5 lbs of seed. I spread mine mixed in fertilizer. When it goes to seed watch it and it will turn a light brown color across the top when the seed have matured. Then go back to grazing. 

My process used to be burndown in late august, spread rye/ryegrass and run over with disc with a chain drag behind to renovate and smooth out.

Ran stockers from fall till summer.  Works well on light soils. There was someone here who did what you are doing several years ago, but the search function won't go back that far now.