If you wanted to buy a new 'vette in 1983, you could. It wasn't the kind built in Bowling Green, KY, though. It was an anemic econobox. With a little tweaking, however, you could make one of them keep up with traffic. Find this '83 Chevette for sale in Birmingham, AL for $3,800 via craigslist.
In the case of this car, a little tweaking means stuffing it with enough cage and reinforcement to handle the torque of a locomotive. With a fuel cell, rear end, suspension and tires to match, this Chevette is almost ready to destroy the 1/4 mile. All it needs is the heart of a champion.
Hopefully the builder of this car paid attention in shop class, as you would not want to find out about poor craftsmanship at the end of a 150 MPH pass. Instead of going all-out, you may want to put a nicely warmed over SBC inside with a Lenco manual transmission. Perhaps you could have something streetable that doesn't need a parachute at the track.
Whatever you decide, you will have something that is definitely not a classic muscle car, not a sleeper, and not something you see every day. Your $3,800 gets you a pretty good start toward what will certainly be a wild ride. Question is: do you have the guts to complete it?