We discuss the convergence properties of chiral expansions for the pseudoscalar and vector charmed meson masses based on the chiral SU(3) Lagrangian. Conventional expansion strategies as formulated in terms of bare meson masses are shown to suffer from poor convergence properties. This changes once the expansion is set up in terms of on-shell masses. We find a rapid convergence of the chiral expansion from vanishing quark masses up to physical values of the strange quark mass in this case. Detailed results are presented at the one-loop level for the $D$-meson and $D^*$-meson masses. It is emphasized that our results do not depend on the renormalization scale. An approximation hierarchy for the chiral Ward identities of QCD is obtained that keeps the proper form of low-energy branch points and cuts as they are implied by the use of on-shell masses. Given such a scheme we analyzed the charmed meson masses as available on various QCD lattice ensembles. In terms of the determined low-energy constants we consider the coupled-channel interactions of the Goldstone bosons with open-charm mesons. For the isospin violating hadronic decay width of the $D_{s0}^*(2317)$ we predict the range $(104-116)$\,keV.