For a lot that size I would be hitting it with some Corn Gluten Meal. 9-0-0 or the liquid CGM with no nitrogen in it.
Timing is very important with CGM. It does help reduce the amount of crabgrass over time (years).
Or 1 application of Acclaim(chemical) and your crabgrass is gone.
Or mechanical removal will help.
Start seeding every fall.