Mapping the QCD phase diagram at large density remains challenging due to the complex action problem in lattice simulations. Using simulations at imaginary baryon chemical potential ($\mu_B$), we observe that, under the strangeness-neutrality condition, both the strangeness chemical potential ($\mu_S / \mu_B$) and the strangeness susceptibility ($\chi_2^S$) take on constant values at the chiral transition across varying $\mu_B$. We present new lattice data to extrapolate contours of constant $\mu_S/\mu_B$ or $\chi_2^S$ to finite baryon chemical potential. These proxies are shown to be only mildly affected by criticality and finite-volume effects, and their continuum limits up to $\mu_B = 400\,\text{MeV}$ agree well with existing determinations of the chiral transition and with the hadron resonance gas model.