Yeah you are in a bit of a situation. I am not sure if I mentioned it to you last night, but my insurance is through Hagerty. I think most insurance companies might link Show Car Insurance with cars being "Classics", which I would assume carries an age stipulation.
I would recommend registering the car in an emissions free area in IL. I am not sure if you will need get the car to pass before you are able to register it in another city/county. I would call the DMV and give them the following story. Say that you will be moving to DeKalb, your car is not running at the moment because you are fixing the emission issue, and you will not have it up & running for a few months. Ask that by the time it is fixed you will already be moved, will it still be necessary to pass emissions?