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I don't think putting all the laws of nature into a hodgepodge that one calls the first postulate is a good idea. To my mind the postulates are supposed to be meta-laws that the observed laws of are to obey. This means that we ought not assume Maxwell's equations a priori before we get the meta-laws down. The way I see it Maxwell's equations *depend on* the Lorentz invariance of SR; they don't dictate that invariance *to* SR (contrary to the formulations of SR that one often sees that takes the constancy of the speed of light as the 2nd postulate of SR).
The way I see things is that SR's Lorentz transformations and the Lorentz invariance of the laws of nature (or a local version of such invariance if we want to accommodate a curved spacetime for GR later) depends on the following two postulates:
P1) The laws of physics (whatever they happen to be, and regardless of which particles may or may not be massless) are form-invariant under transformations among the equivalence class of (local) inertial reference frames.
P2) There is no such thing as instantaneous-interaction-at-a-distance.