We present extended X-ray absorption fine structure (EXAFS) spectra and modeling of a series of structurally tunable quasi-one-dimensional mixed-valence platinum-halide linear chain materials, [Pt(en2)][Pt(en2)X2](ClO4)4 with X = Cl, Br, I. The materials exhibit a commensurate charge density wave with fractional charge states on alternating platinum ions in the chain, as well as a Peierls distortion with alternating platinum-halide bond lengths. The amplitude of the charge density wave and, correspondingly, the extent of the Peierls distortion are controlled by the identity of the bridging halide ion. We have carried out ab initio multiple scattering calculations using the FEFF9 code to relate the oriented Pt LIII EXAFS spectra to the tunable electronic and structural properties. The spectral modeling reveals distinct photoelectron threshold energy values for the two inequivalent platinum ions in each of the mixed-valence chains, with values that vary systematically with fractional valence state. The difference in the photoelectron threshold energies of the two inequivalent platinum ions within each material correlates directly with the amplitude of the charge density wave, reflecting the decrease in charge density wave strength through the halide series X = Cl, Br, and I. We use dynamical matrix modeling to relate the experimentally determined mean-square relative displacement parameters for the metal-halide bond distances to the chain-axis vibrational modes that modulate the charge density wave structure. In addition, we discuss the EXAFS fitting results for the Pt-I bond lengths in the [Pt(en2)][Pt(en2)I2](ClO4)4 complex in comparison to previous, mutually inconsistent structural determinations for this material.