I've lived in Illinois my entire adult life, and have never been asked by anyone if my address was current on my FOID card. As long as you take care of the change of address notification only an over-zealous knot-head would make any kind of issue about it. The trouble is we do have a few of those running loose...you just have to deal with them as they come.
Fill out your paper work with your current address and enjoy your purchases.