We examine the constraints imposed by helioseismic data on the solar heavy element abundances. In prior work we argued that the measured depth of the surface convection zone R_CZ and the surface helium abundance Y_surf were good metallicity indicators which placed separable constraints on light metals (CNONe) and the heavier species with good relative meteoritic abundances. The resulting interiors-based abundance scale was higher than some published studies based on 3D model atmospheres at a highly significant level. In this paper we explore the usage of the solar sound speed in the radiative interior as an additional diagnostic, and find that it is sensitive to changes in the Ne/O ratio even for models constructed to have the same R_CZ and Y_surf. Three distinct helioseismic tests (opacity in the radiative core, ionization in the convection zone, and the core mean molecular weight) yield consistent results. Our preferred O, Ne and Fe abundances are 8.86 +/-0.04, 8.15 +/-0.17 and 7.50 +/-0.05 respectively. They are consistent with the midrange of recently published 3D atmospheric abundances measurements. The values for O, Ne and Fe which combine interiors and atmospheric inferences are 8.83 +/-0.04, 8.08 +/-0.09 and 7.49 +/-0.04 respectively.