Remember, they won't pull you over unless you give them a reason. If you obey the traffic laws and keep within a reasonable range of the speed limit, you probably won't get stopped. Good rule of thumb if you have guns in the car is to stay within 5mph of the limit (slower than you would drive without guns). You can control how you drive, but you can not control the unexpected. Never know when your car might break down, or if you might unfortunately be involved in an accident. If you need an ambulance ride, don't be surprised to find out later that your car was searched. If you're in an accident, or break down, the cops will likely be peering into your car, so make sure your gun cases and accessories are out of sight and the chances of having a gun-related conversation will be a lot less. Follow IL law and keep the guns in locked cases just in case they happen to be spotted by a trooper.
Your best bet is to avoid Illinois like the plague it is. Take the extra time to go around it, fly into an airport in a neighboring state. If your destination is unfortunately in the state of Illinois, be prepared to feel naked and a couple pounds lighter as you go about your business dis-armed.