Of course it can be stable but I think you would definitely want to play with it a little in the 10s-12s first.
The old cars will be a bit easier too because it isn't turning the entire wiring system and drivetrain on its head.
If you build a race car, it's a race car. The one thing that would be a lot more effort is converting to rear wheel drive, other than that, the effort would be about the same for most any car.
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'67 Dart 270 4 door '72 340(9.5:1), 727, 8-3/4", A/C, original interior, big bolt discs
'77 Aspen SE 2 door '77 318, 998,8-1/4",A/C, Cruise control car,power discs,power steering