Not sure how cogent this is to the original post and followup question, but IL is a SEMA state. Replicas can be legally titled and registered as a vehicle manufactured in the year the car replicates (once all the appropriate hoops are jumped through). So, if you have a manufacturer's certificate of origin (something any builder should be able to produce), you can register as a '5X replica. CA has the SB100 registration which, if I'm not mistaken, allows the title to be written for the year the car replicates (kind've a modified SEMA deal).
In my state, at least, the allows me to run antique plates. There are all kinds of crazy restrictions on usage for these plates (only for driving to shows, parades, etc.), but I've driven to the west coast twice on them, been stopped half a dozen times, etc., and never had a problem.
Robert can speak more intelligently than I can about this, but I figure: being improperly titled and registered is a possible impound of the car if I catch a cop on a bad day. Improper usage? That's a $120 ticket, and no points on the record. Given that the differential between the cost of antique tags and regular tags is about $125/yr, I'll risk it. Traveling out of state on these plates is even less risky-- I've proven that Nevada (at least) cops have no desire to learn the esoteric idiosyncrasies of Illinois registration laws-- they just run the plates and if they come up good, they'll write the speeding citation (or not) and send you on your way.
I would imagine that displaying the wrong plate while having the right titling is something that nobody is ever going to write up. If they do, they do. I'm OK with that as long as no points are involved. I always try to look at risk/return-- if the downside exposure costs less than the upfront cost, it's hard to make an argument for abiding by the (revenue generating ) letter of the law. If the downside is a risk I'd rather not run (getting my car impounded or potentially crushed as happened to some improperly titled Cobras), then I'll dot every "I" and cross every "T" no matter what it costs.
I know CA is different, in that plates follow the car not the owner-- but I can't imagine that displaying 1957 plates on an SB100 registered car is going to get any worse than a small fine at the worst, and a nice conversation at the best. I've been pulled over several times just so the cop could talk about the car with me. A cool car is a cool car, and cops are people too.