Impy, if you want Illinois to change their primary system, please write to some state legislators and ask them to change it. In Feb. 2002, I heard a radio talk show host, Joe Gentile, say, “I want to vote for John Cox, for the U.S. Senate, and Paul Vallas, for governor, but I can’t do that because Illinois has a stupid primary that forces people to choose a party, for a primary.”
The system I described, used at the time in California, was ruled to be unconstitutional by the Supreme Court in 2000.
https://en.wikipedia.org/wiki/California_Democratic_Party_v._Jones
I actually am forced to agree with the decision on legal grounds, and it would be horrible for conservatives if Republican states had such a system, but that doesn’t stop me from wishing I could have my cake and eat it too.