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We propose a Standard Model extension, coined VISH$\nu$ (Variant-axIon SeesawHiggs $\nu$-trino), that is an $N_{\text{DW}} = 1$ variation of itspredecessor, the $\nu$DFSZ model. In accounting for the origin of neutrinomasses, dark matter and the baryon asymmetry of the universe, VISH$\nu$inherits the explanatory power of $\nu$DFSZ while, of course, resolving thestrong $CP$ problem. In both models, the electroweak scale is naturallyprotected from a high seesaw scale that is identified with the Peccei-Quinn(PQ) spontaneous symmetry breaking scale. Through a flavour variant couplingstructure, VISH$\nu$ evades a domain wall problem, extending the cosmologicalreach of the $\nu$DFSZ to include a viable period of inflation. The primaryfocus of this paper is on the inflationary dynamics of VISH$\nu$ and theirnaturalness in the sense of radiative stability. We find that non-minimalgravitational couplings, generically developed by the VISH$\nu$ scalar fields,naturally support a viable inflaton field which typically has both a PQ scalarand Higgs component. An axion mass window [$40\mu\text{eV}, \sim 2\text{meV}$]accessible to forthcoming searches, results for the case where PQ symmetry isrestored during the (p)reheating phase.

VISH$\nu$: a unified solution to five SM shortcomings with a protected electroweak scale