You might want to print out a copy of the federal law that states you can legally transport in unloaded in a locked case in the trunk. Not saying that will keep police harassment at bay but it might look like you were really trying to follow the letter of the law which you will be doing. Another thought is to disasemble the gun right prior to state lines. This may look "better" to the officer. Just remove the slide from the frame and keep everything else intact. Lock it in the box while transporting through ILLI-Nazi. Once you reach a gun friendly state, reassemble, reload and go about your merry way.
ILLINOIS--A nonresident is permitted to transport a firearm provided it is unloaded, enclosed in a case, and not easily accessible. A nonresident may possess a firearm for licensed hunting, or at a Department of Law Enforcement recognized target shooting range or gun show.
The City of Chicago requires all firearms possessed in the city to be registered. Handguns not previously registered in Chicago cannot be registered. Oak Park, Evanston, Morton Grove, Highland Park, Wilmette, and Winnetka prohibit the possession of a handgun. Firearms may be transported under the general rule through Chicago for a lawful recreational firearm-related activity.