There are some weed killers that now act as just that plus a pre emergent week stop. Of course if you break the soil in your case that will defeat it. I detest cloverI'm working with Kentucky Blue grass. So far I've put down Spectracide weed killer in March. I then made the mistake of dethatching and now some areas have dandelions and clover.
I'm thinking about applying more Spectracide weed killer this weekend. Also need to work on seeding some small areas.