Is Special Relativity Really Tested Empirically

All elements of special relativity, like the Lorentz transform, time dilation, space contraction, moving mass and E=mc^2 are said to be verified empirically beyond any doubt. While checking a discrete model of space I was surprised to notice that these experiments cannot distinguish between the Lorentz transform and the coordinate transform in my discrete model. There were also a lack of clarity in what frame of reference the formula for moving mass is differentiated to give E=mc^2. In the discrete model E=mc^2 follows easily from basic concepts. My conclusion is that the special relativity theory is not tested well enough and the principle that there is no preferred frame of reference should be revised.