I saw a magazine article that was comparing the mustang, corvette, and GTR on a track with a professional driver and full race logging gear. The mustang was handicapped by the absurdly stupid solid axle that they still put in them. It could hang in the straights and even catch up a little but it lost so much in the corners that it really didn't matter.

Build a light car with a full cage and fully modern and sorted independent suspension and modify it enough to put big tires under it. In the end you'll end up with something akin to the '64 Plymouth that Everham motorsports just did. It will have the outer look of an old car, but it will not be the same car at all.