I don't like that 'popularization', because the ,wavelength of light is much longer than the distance between atoms. This means the light wave interacts with a large numberr of atoms coherently, and not with indivudual scattering. You must use the derivation you gave, which is still simpler than the full derivation.

The scattering description loses the vital point that it is wave propagation.

How to describe dispersion to high school students? Considering I wasn't exposed to this really until graduate school, that's a tough one. I think you're approach does a decent job.

My (paraphrased) understanding of the perturbation theory approach is that a photon interacts with an electron in the ground state exciting it up to a "virtual state", which is related to the nearest real excited state. Because the energy of the photon does not match the energy difference between the ground state and the real excited state, this "virtual state" has a lifetime limited by the uncertainty principle based on this energy mismatch (detuning). The electron then decays back down to the ground state re-emitting the photon, but with a slightly different phase, based on the lifetime of the "virtual state". Since the phase is shifted, it appears as if the wave has been retarded somewhat, resulting a slower phase velocity, and thus refractive index greater than 1. The lifetime of the "virtual state" is inversely proportional to the energy mismatch, so that for photon energies closer to resonance, the phase shift is larger, resulting in an even greater refractive index.