My rule of thumb is to never do something that can't be changed back. The most radical thing I've ever done is switched out a drivetrain, because the motor had a cracked block. I tend to leave my stuff stock, or change things that can easily go back. It gives a wider market and that way you're not 'wrecking' an original.
Chopping, channeling, dechroming, removing all door handles, adding fins, replacing single head lites to duels, custom tail lites, different grille, dash, gauges, lowering, drivetrain, etc. can all be changed back. You just sell the thing and buy another original. Have fun. You only go around once. Anything can eventually be shown at the Wal-Mart car show!
Oh man! I love tailfins and that's why I bought a '58 wagon. Ford wagons lost them in 1963 so the last year of the tailfin was '62 on the full size cars and the Fairlane midsize. Most Ford body styles all the way up to 1970 ran a sharp body crease along the top of the fenders. To create some sort of "vestigial fin" from this crease would keep the design from looking too tacked on. And might actually improve the look. I know that the Fairlanes in '64 look almost nekid in the back due to the loss. Go for it and damn the rarity! (Hope you know how to weld.)
Looks like some Mopar designers were taking your advice and checking out this model kit and using it for their '70 Plymouth Sport Fury