As a Chicagoan I'm been fighting the front plate ticket for many years... Below is the solution that I created in order to have a plate displayed while parked on the public streets and removed the rest of the time. I bought all the pieces from Home Depot for under $10.
Suction Cups - 54402 Home Depot
Razor Blade to cut tape
Back of the plate with suction cups and felt tape
Close up of Front Plate
Front Plate with Suction Cups