Sorry all, but the impedance of free space is set by the choice of units. If you use natural or Planck units where c and H bar and other constants are 1, the Planck impedance comes out to be about 30. More to the point, Planck units sets Coulomb's constant 1/(4 X pi X epsilon zero) = 1. This represents a choice of units. 

To the point. If instead you set the permitivity epsilon zero = 1, along with c=1, then the permeability mu zero is also 1, and the impedance of free space is also 1. 

It is simply units, there is no physics behind the 377 ohms. 

See Wikipedia at https://en.m.wikipedia.org/wiki/Planck_units