I see a problem with the size of the area. No groundcover will be so thick it will choke out grass or other wind borne seeds. After a while you will be looking at weeding and with the size of the area this means wading in. Tough...
White clover is an excellent idea from @woodchips. I have used it to open up and enrich thick clay soil. There are other groundcovers that can compete with grass like creeping thyme although it prefers hot and dry areas.
Another idea which will cost you more in the short term but be very effective is to use Rhus aromatica cultivar 'Gro-low'. This cultivar of this shrub spreads six feet and grows three feet tall. It is great low maintenance plant for mass beds or bank control with fragrant leaves. I see that some kinds of sumac grow where you live so check your local nursery for availability.
To use this you would sow white clover and plant the rhus on five or six feet spacing. If your area was fifty feet by twenty feet you could buy thirty plants and have the job done. The clover would enrich the soil and keep out weeds while the sumac establishes.