You would have to plant things that would overtake the grasses, easier said than done.
One way to manage pasture like that is to have a controlled burn on it. I rather doubt you can do that to a private garden in New Jersey, though. You might consider getting someone to hay it for you, perhaps in broad swathes around islands of butterfly attractants you want to keep.
You could also try solarizing very grassy areas and replant at the end of summer.
Another similar approach would be to use heavy mulch on the mown grasses. If you spread straw or pine bark or wood chips pretty thickly it would starve the grasses below it, and enrich the soil as it breaks down.