Pull it all out right now, it will take 1-2 hours and is not that difficult.
Get to the center of each plant and pull each plant out completely. I simply find the center root on a small plant, or gather up all the horizontal stems together and pull from as close to the soil as I can. You want to pull the roots out so that they are not emitting a chemical which makes it difficult for other grasses to grow.
I realize this is the organic thread but look...that's a very small plot of grass. You should water it so that it is not dormant. There is no way your grass can compete if it's dormant against that stand of crabgrass.
Do not leave it, don't just whack it, you gotta pull it. You're an organic guy come on pull it up!
I have a front yard 2x that size, i can speak from experience it will be 1-2 hours for you to pull it all. Once you do, commit 15 minutes a week to sweeping across the lawn and pulling any newbies trying to come up.