We report on salient features of a mixed lattice QCD action using valence Möbius domain-wall fermions solved on the dynamical \(N_f=2+1+1\) HISQ ensembles generated by the MILC Collaboration. The approximate chiral symmetry properties of the valence fermions are shown to be significantly improved by utilizing the gradient-flow scheme to first smear the HISQ configurations. The greater numerical cost of the Möbius domain-wall inversions is mitigated by the highly efficient QUDA library optimized for NVIDIA GPU accelerated compute nodes. We have created an interface to this optimized QUDA solver in Chroma. We provide tuned parameters of the action and performance of QUDA using ensembles with the lattice spacings \(a\simeq{0.15,0.12,0.09}\) fm and pion masses \(m_\pi \simeq{310,220,130}\) MeV. We have additionally generated two new ensembles with \(a\sim0.12\) fm and \(m_\pi \simeq{400,350}\) MeV. With a fixed flow-time of \(t_{gf}=1\) in lattice units, the residual chiral symmetry breaking of the valence fermions is kept below 10\% of the light quark mass on all ensembles, \(m_{res}\leq0.1\times m_l\), with moderate values of the fifth dimension \(L_5\) and a domain-wall height \(M_5\leq 1.3\). As a benchmark calculation, we perform a continuum, infinite volume, physical pion and kaon mass extrapolation of \(F_{K_\pm}/F_{\pi_\pm}\) and demonstrate our results are independent of flow-time, and consistent with the FLAG determination of this quantity at the level of less than one standard deviation.