ERRATA:
The above claim is incorrect!!!
I finally found the correct way to demonstrate invariance. I had done the derivation from scratch once as a homework assignment, but that was 12 years ago. I lost my notes, but I found a comparable derivation on the net and have to adapt the notation and symbols and conventions. Using the symbol conventions above, what I need to show is that under the Lorentz transformation is that assuming:
\LARGE \frac{\partial E}{\partial^2x} = \mu_o \epsilon_0 \frac{\partial^2}{\partial t^2}
under the Lorentz transformation
\LARGE \frac{\partial E}{\partial^2x'} = \mu_o \epsilon_0 \frac{\partial^2 E}{\partial t'^2}
Apologies to the reader. I will put an edit in the original comment to point to this correction.