Why?

-It's pretty much gonna start without having to worry about chokes, flooding, washing down the cylinders with raw fuel, etc.

That's an easy fix with something like an ez efi kit. Gonna be close to a grand to buy and install it right though.

Is a 68 Barracuda still a 68 Barracuda with a modern drivetrain, sound insulation, big wattage system, leather interior, temperature control, etc.?

Damn right it still a 68 barracuda. It's just what it would have been if all the tech was avalible back then. Nothing wrong with improving a car.