I'm def not 460 expert but do know there internal and externally balanced 460s and the flywheel can be part of the balance. I'd ask your friend if he knows which it is, or can contact his builder.
While schooling myself I came across this.
460 Internally or externally balanced - Ford Truck Enthusiasts Forums
But since I'm also a firm believer in what did you touch last troubleshooting....
1) Press the pedal to the floor and rev the engine to around to the the rpm you witnessed the vibration at. Do you feel a vibration? If not, it is not the flywheel pressure plate, internal engine components, or the harmonic balancer. If there is a vibration, you either have the wrong flywheel, it is machined wrong and has excessive runout, the pressure plate is out of balance, or it is off center. Do you feel pedal pulsation? If it moves up and down with it pressed, it is a good indication of misaligned parts. Was the flywheel seated against the crankshaft properly and torqued evenly?
2) If there was no vibration in step one, release the pedal allowing the disc to spin with the flywheel and pressure plate and rev the engine again. If there is a vibration now, either the clutch disc is out of balance, or there is a problem with the pilot bearing allowing the clutch disc and input shaft to spin off center. Lightly press the pedal allowing the throw-out bearing to press against the flywheel. Feel any pedal pulsation? Once again, a good indication of misaligned parts. Was the pressure plate tightened evenly?
3) Is the vibration isolated to driving? If so, look at the driveshaft. Was it dropped and dented? this can cause vibration while driving. If the crossmember or mount isn't installed properly driveline angles can be off causing the vibration. Wear in the universal joints? I doubt it since almost all Cobras are rarely driven and typically over maintained when compared to a normal vehicle.