I have a Lone Star and it's titled as a 2000 Cobra, the year it was made. It was titled here 5 years before the new "year it represents" law came into effect. Virginia has actually become quite easy on the replica crowd. You might be able to argue that it represents a 66 and get the Virginia DMV to buy in. They're probably going to make you title it as the same year the old title had it as though. Get all your paperwork together and take it to the DMV for an initial visit. They'll give you exact instructions what to do from there.
I bought my car as a driver from a guy in South Dakota. It came with a MSO and a 2000 title. I did not have to do the state police thing on mine when I titled it here. I've never had any problems with emissions requirements for state inspections in my part of Virginia. They don't sniff tailpipes in my area either. They do in other parts of Virginia though, typically the northern and western parts of the state. Us southern boyz get a free pass
Also, If you get them to title it as a 66 you can get some original Virginia 1966 plates (FleaBay or otherwise) and register it with them. That definitely adds to the cool factor. It will require it to have "antique plates" which Va places some restrictions on what you can do with the car, mileage, where you drive it, etc...