HF school district is a blue ribbon and your credit and income is a factor. Never the less, if you give me a call I do have some homeowner in the district that might look at renting. My office number is 708-922-1055.
I am a Flossmoor agent and work with area rentals quite often. Getting into a rental in the HF school district is challenging, but certainly can be done. Feel free to contact me. I can set you up for a free search so you will be among the first to see any new rental listing. We can also discuss other options for you and your family.