I didn't have the probem as my car carries a 1966 Ford VIN, but in your case you're probably going to have to bite the bullet and just go with having it compliant. Word on the street is that the DPS is not happy with the automotive enthusiast contingent and that in the near future there will be crackdowns.
I think I'll change my replica to a Kansas title/registration. When I do that I can buy "Antique" plates for the car ( one time fee of $17) and thereafter I don't have to pay for the "registration" part of the road fees from then on, only the property tax part (yes, KS does levy property taxes on vehicles, but in the case of my Honda Accord the overall cost of the registration is very close, maybe just a very small bit higher in KS). Kansas has no usage restrictions, unlike TX, for "antique" plates.
I think we ought to start lobbying our state legislators to adopt the SEMA registration plan, a lot of states have done so already (but, then, you know how our governor likes to maintain his "independence", so I suspect it would be a hard sell right now).
There's a "registration" forum on the site, I'll come back and add a link as an edit.
Registration Forum - Club Cobra
Cheers, Dugly