It seems Illinois has a sizable Guard aviation unit. You are going to probably want to find a unit that is closer to where you live, rather than just in your state. Guard aviators are expected to go in weekly to fly in addition to drilling.
Reach out to an Illinois guard recruiter and have him get you in touch with the "Warrant Officer Strength Manager." The WOSM will be able to get you information directly about what your state requires for prospective aviators. It varies state by state -- some allow anyone off the street to apply, others require you to have current membership in the Guard, and others do something somewhere in the middle or are willing to work with potential aviators. When you talk to the WOSM, have them get you in touch with someone at the aviation unit directly so you can talk to them, meet them for coffee, and generally get yourself on their radar. If Illinois is willing to consider you, go from there. They should advise on what you need for a packet/how they want it put together. Also, your recruiter can tell you what you need from the USMC, it will be some form of conditional release.
If you can get a secret clearance started if you don't already have one while you are still USMC, that would be helpful. There's a good chance if you're a 31 you don't have one. You will also need a class 1 flight physical approved by Ft Rucker, as well as a SIFT test score.
As to the process... assuming Illinois boards you and accepts you on the condition the USMCR gives you a conditional release, you'll probably separate from the USMC after boarding and being accepted by the Guard, and start drilling as a warrant officer candidate with the aviation unit until they get you school seats. You won't be required to go to boot camp, but you will have to attend WOCS, and then about 14-18 months of flight school which includes (if you haven't done it already) SERE-C. They won't typically split it up from what I understand, but often there is a bit of a gap between WOCS (which is looking like will be 4.5 weeks for all classes pretty soon) and flight school, and often there is not.
You need not go to "your" state's Guard unit... just keep in mind you're going to need to go in weekly to fly, so consider the commute.
There seem to be a lot of Marines who go this route FWIW. I was an 0331 in the reserves from 08-14. I'm a "WOC" in the Guard now waiting for school dates. It's a very different world from being an 0331 in the Marine Corps. So far, much less yelling and much happier people. Not sure what your experience in the SMCR has been like, and though I generally had a good experience, the Guard seems to care much more about it's members' civilian lives and careers. Your mileage may vary, of course.