Pick up the phone and become somebody's nagging pain.
A few years ago I had a problem getting a timely renewal of my IL FOID. I have a fairly common name and the initial computer check showed 49 felons with same/similar name which then required human review to compare addresses, race, birthdate, etc to verify that I was who I said I was. I had applied for the renewal with plenty of time but I called ISP firearm division when I was a couple weeks from the date on my card. I was told that they had a backlog and just to wait a little longer. The day before my card expired I had the day off and still no card. I called again and was told just to keep my firearms locked up at home and unloaded and I would be OK (even though I could have been charged with unlawful possession!) This really P'd me off so I spent an afternoon calling my reps and state senator's offices, the governor's office, the DNR and ISP, and the ISRA. I wound up talking to the director of the ISP FOID-whatever division and had a spirited but polite debate with him for 15 minutes. Got assurances that my app was being fast-tracked and had my card in 4 days.
Seriously, if you are not getting the service from these public servants get on the phone and start bichin and keep bichin until they do something! It does no good to whine here does it?
Oh, and while you got them on the phone... Let them know its time to VOID the FOID in Illinois!