We present a lattice-QCD calculation of the masses and decay constants of the positive-parity heavy-strange mesons $D^*_{s0}$, $D_{s1}$, $B^*_{s0}$, and $B_{s1}$. The calculations are performed with domain-wall fermions for the light and strange quarks and an anisotropic clover action for the charm and bottom quarks. We use seven different RBC/UKQCD ensembles with pion masses ranging from a near-physical 139 MeV up to 431 MeV. We consider two different analysis types, with or without two-meson operators at the source. We observe the expected below-threshold ground states. The fits without the two-meson operators appear to be more stable, but may overestimate the ground-state energies, while preliminary fits with two-meson operators at the source only appear to underestimate the ground-state energies.