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A Standard Model extension is proposed, coined VISH$\nu$ (Variant-axIon Seesaw Higgs $\nu$-trino), that is an $N_{DW} = 1$ variation of its predecessor, the $\nu$DFSZ model. In accounting for the origin of neutrino masses, dark matter and the baryon asymmetry of the universe, VISH$\nu$ inherits the explanatory power of $\nu$DFSZ while, of course, resolving the strong CP problem. In both models, the electroweak scale is naturally protected from a high seesaw scale that is identified with the Peccei-Quinn (PQ) spontaneous symmetry breaking scale. Through a variant flavour coupling structure, VISH$\nu$ evades a domain wall problem, extending the cosmological reach of the $\nu$DFSZ to include a viable period of high-scale inflation. The primary focus of this work is on the possible inflaton configurations of a class of three-scalar models and when these preserve natural features of VISH$\nu$. We find that non-minimal gravitational couplings, generically developed by the VISH$\nu$ scalar fields, support a viable inflaton field which typically has both a PQ scalar and Higgs component. An axion mass window [$40\mu$eV, $\sim 2$meV] accessible to forthcoming searches, results for the case where PQ symmetry is restored during the (p)reheating phase.