In Illinois, you can run a plate from the year of the car. I'm pretty sure they don't specify WHAT state, so you could technically run a plate from any state of the same year. Since '83 was a sticker in a lot of places, you could probably run just about any plate, and just get an '83 sticker. As long as you have the AV plates and registration in the car, you're ok. Also, one of the allowed uses of a car with AV plates is for "demonstration". No matter where I go, someone says "nice car" and asks me about it. I classify this as a "demonstration".
Interestingly, I find that I get almost zero law enforcement attention when I'm driving one of my AV cars. It's almost like there's an unwritten rule to just ignore them. When I was younger and drove much milder cars, I was getting pulled over on a monthly basis, usually for no good reason. Now, I don't even run a front plate, and it's like I'm invisible.