2659 E 74th is for sale (2 story home)
6741 S Bennett is for sale (2 story home)
7525 S East End (further South but ranch style like 6829 S Constance) is for sale
6740 S Paxton is for sale too
I can help you purchase any of these home and point you in the right direction to get assistance from the State of Illinois.
Feel free to contact me Jeff Nobleza with Baird & Warner 773 677 5340 Jeff.Nobleza@BairdWarner.com