Models of solar-like oscillators yield acoustic modes at different frequencies than would be seen in actual stars possessing identical interior structure, due to modelling error near the surface. This asteroseismic surface term must be corrected when mode frequencies are used to infer stellar structure. Subgiants exhibit oscillations of mixed acoustic ($p$-mode) and gravity ($g$-mode) character, which defy description by the traditional $p$-mode asymptotic relation. Since nonparametric diagnostics of the surface term rely on this description, they cannot be applied to subgiants directly. In Paper I, we generalised such nonparametric methods to mixed modes, and showed that traditional surface-term corrections only account for mixed-mode coupling to, at best, first order in a perturbative expansion. Here, we apply those results, modelling subgiants using asteroseismic data. We demonstrate that, for grid-based inference of subgiant properties using individual mode frequencies, neglecting higher-order effects of mode coupling in the surface term results in significant systematic differences in the inferred stellar masses, and measurable systematics in other fundamental properties. While these systematics are smaller than those resulting from other choices of model construction, they persist for both parametric and nonparametric formulations of the surface term. This suggests that mode coupling should be fully accounted for when correcting for the surface term in seismic modelling with mixed modes, irrespective of the choice of correction used. The inferred properties of subgiants, in particular masses and ages, also depend on the choice of surface-term correction, in a different manner from both main-sequence and red giant stars.
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