We performed tunable resonance Raman spectroscopy on samples highly enriched in the (5,5), (6,6), (7,7), and (8,8) armchair structures of metallic single-wall carbon nanotubes. We present Raman excitation profiles (REPs) for both the radial breathing mode and G-band phonons of these species. G-band excitation profiles are shown to resolve the expected incoming and outgoing resonances of the scattering process. Notably, the profiles are highly asymmetric, with the higher-energy outgoing resonance weaker than the incoming resonance. These results are comparable to the asymmetric excitation profiles observed previously in semiconducting nanotubes, introduce a different electronic type, and broaden the structural range over which the asymmetry is found to exist. Modeling of the behavior with a third-order quantum model that accounts for the k dependence in energies and matrix elements, without including excitonic effects, is found to be insufficient for reproducing the observed asymmetry. We introduce an alternative fifth-order model in which the REP asymmetry arises from quantum interference introduced by phonon-mediated state mixing between the EM11 and K-momentum excitons. Such state mixing effectively introduces a nuclear coordinate dependence in the transition dipole moment and thus may be viewed as a non-Condon effect from a molecular perspective. This result unifies a molecularlike picture of nanotube transitions (introduced by their excitonic nature) with a condensed matter approach for describing their behavior.