This.
I put 40 or so in a gallon zip lock. Spray liberally with “One Shot”. Shake & roll around, spray till they are coated nicely. Resize.
Fast & Effective.
I don’t know about that big of a field, but on my lawn Dimension pre-emergent herbicide works well.
You put it down in early spring before the broadleaf weeds sprout. Doesn’t kill the lawn, just prevents weeds from coming up...