A street rod can be had with that modern drivetrain... plus better suspension, steering and brakes... A/C... etc, for less than you could build it yourself.
You could repaint it in early style colors, if necessary... then add something like aftermarket wire wheels, to give it a vintage look. Check out "thewheelsmith.net".
That would also allow you to use modern tires. A customer of mine is doing a '30s vintage-appearing project right now.
Cheaper and faster than rebuilding an original car. :-)