The best estimate I've read is that electrons in an "electric conductor" move in an electric current
[shifting from one electron-hole to another] at 10 percent of TSOL, more-or-less. If they moved at
say 20 percent of TSOL in a conducting wire there would be obvious relativistic effects.

Sorry, the electrons in metals never get even close to that velocity in conduction. For an average electron try mm/min as a first guess. The electric field propagates via electron interactions at about .6c. It's easy to measure with simple lab equipment. It's an electric field carrying the signal. Think of it as composed of photons of near infinite wavelength. Besides, opacity doesn't matter because the signal is carried on the surface of the conductor.

Larry's links would be useful here. Try reading them.