The quasiskutterudite superconductors A(3)T(4)Sn(13) 9A = Sr, Ca; T = Ir, Rh, Co) are highly tunable, featuring a structural quantum critical point. We construct a temperature-lattice constant phase diagram for these isovalent compounds, establishing Ca3Rh4Sn13 and Ca3Co4Sn13 as members close to and far away from the structural quantum critical point, respectively. Deconvolution of the lattice specific heat and the electrical resistivity provide an approximate phonon density of states F(omega) and the electron-phonon transport coupling function alpha F-2(tr)(omega) for Ca3Rh4Sn13 and Ca3Co4Sn13, enabling us to investigate the influence of the structural quantum critical point. Our results support the scenario of phonon softening close to the structural quantum critical point, and explain the enhancement of the coupling strength on approaching structural instability.