Local Lorentz Invariance and Conformal Metric Transformations It is often repeated that Lorentz invariance of Special Relativity (i.e., allowed solutions to Maxwell's Equations) is proven experimentally.  This is clearly the case for local experiments and transformations between locally defined inertial frames. 
My question is: 
To what extent a conformal metric transformation that alters the Minkowski metric but 
(a) converts solutions to Maxwell's equations into solutions defined with respect to the transformed space-time), 
(b) everywhere preserves local Lorentz invariance (within the limits of experiment), and 
(c) leaves the total energy of the field invariant violates Special Relativity or is excluded by experimental evidence?  
 A: Saying the Lorentz invariance is the allowed solutions to Maxwell's equations is odd. Solutions to Maxwell's equations are Lorentz invariant. Electromagnetism (EM) is not the sole evidence for Lorentz invariance. It is also demonstrated experimentally by clocks in motion.
I am not entirely sure of your exact question. Do you mean, to what extent does a conformal transformation as a symmetry that [...] violates Special Relativity?
EM is invariant under the conformal group, unless you add charged particles, in which case scale invariance is broken. So your a) and c) parts are accounted for.
Now, to address your question. First, regarding experimental exclusion, there could never be absolutely real experimental work with conformal invariance. What I mean by that is that the introduction of your measurement apparatus introduces a scale in the experiment which breaks conformal invariance. Conformal theories are somewhat idealized but are used as limit case in the study of real phenomenon, e.g. in condensed matter.
Now, as to the violation of SR, if you posit a conformally invariant theory with a massive spectrum of particles, you will encounter problems with SR. Otherwise, nothing obvious comes to mind. If you consider gravity, then many subtlety arises. For instance, is EM really conformally invariant at high energies when the possibility for geons (bound state of gravity and EM fields) exists. In any case, in extremely curved space, Lorentz invariance becomes more and more meaningless since a local neighbourhood is less and less Minkowskian. What is a translation in curved spacetime?
