However, we do live in a town with mowing ordinances. Georgette and Kyle Jones Montevideo, MN Hello Joneses, Sad to say, there is no magic seed you can scatter, and that will spring up in low grasses or ground cover and crowd out your meadow sod plants. It is at minimum a two-year job. The best way is to cut out the sod, roots and all, with a rented power sod-cutter. Roll up, remove and replant the sod on bare soil or stack upside-down under a tarp and compost it.
Fabric lasts longer, but costs more than paper.
Don't use black plastic mulch. It won't biodegrade, but will shred and blow around and have to be taken up in a year or less. Plant ground cover cuttings through the black sheet mulch. You can sprinkle on straw or grass mowings to camouflage the black color. For less cash outlay, you can substitute multiple layers of newspaper for the black mulch.