I lived in Troy Ill for quite a wile - just across the river. I recall
a master gardeners lively discussion on the subject.

Normal temps during growing season - one inch water per week. If temps
go into the mid nineties - 1 1/2" per week; 100's - 2".

Raise mower to 4-6" in very high heat by buying bigger wheels. The prof
said that a wheatfield at 2 or more feet looks great; its the even cut,
not the height, that looks good. [Shorten gradually as weather
improves]

Rain falls at night and doesnt mold unless its a looong duration. Its
more important to water every 3-4 days, deeply- [1/2" or more each time
in high heat]. Especially the sunny areas. Place tuna cans around to
see how long it takes to get a half inch.

I bought traveling sprinklers- Sears was better than Nelson [jumped
regular size hose so had to by fat ones and gave less water per hour].
Set up the night before, they could be turned on in the am while getting
ready for work.

A warning - I tried to beat the 11:00am watering deadline for heat- even
at 10am, I started a grass fire, and even set afire a wooden stake!!!
The fire dept said that that is how many grass fires start.

I understand that grasses with 5-ft roots are available- maybe they are
on display at the seed places - there is one in Belleville that grows
grass samples - and might mix well with what you have.

Hey-now Im in Florida - its cooler than you are- hmmm.