::You are right about Heaviside-Lorentz. I failed to take account of the difference between Heaviside-Lorentz rationalization and MKS rationalization (the latter called Fessenden rationalization in D.L. Cohen, Demystifying Electromagnetic Equations). 
 ::As for E/H, I was merely indicating that it is the basis for the stated values. In fact, I have failed to find any reference in a selection of textbooks to "the impedance of free space" other than in SI units. Note that in SI, circuit impedance V/I and wave impedance E/H both have the same units as resistance, whereas in Gaussian units the former still does but the latter is dimensionless. So in Gaussian units it is at best confusing to call both quantities impedance. It would certainly be worth attempting to interpret 377 Ω in SI physically, as you suggest, and then asking what the corresponding physics is in Gaussian.