We present next-to-leading-order (NLO) calculations of heavy-quark contributions to deep-inelastic scattering (DIS) structure functions $F_4$ and $F_5$ within the Aivazis--Collins--Olness--Tung (ACOT) scheme, implemented in the open source library \texttt{APFEL++} using \texttt{CT18NLO} parton distribution functions. These structure functions, suppressed by lepton mass effects in light-lepton processes, become significant in muon, tau-lepton and neutrino scattering at facilities such as SHiP, IceCube, and DUNE. Our results reveal NLO corrections up to 10\% relative to leading order, with pronounced heavy-quark effects at low Bjorken-$x$, impacting gluon and strange quark distributions. In the unpolarized case, $F_{4/5}^{\gamma Z}$ and $F_{4/5}^{\gamma}$ do not contribute to the cross section, while the $\gamma Z$ interference becomes accessible with longitudinally polarized lepton beams at the Electron-Ion Collider (EIC), offering enhanced sensitivity at low $Q^2$ due to reduced $Z$-boson propagator suppression. Analytical NLO expressions have also been derived for the polarized structure functions $g_1$, $g_4$, $g_5$, $g_6$, and $g_7$ in the ACOT framework. These developments enable precise theoretical predictions for upcoming experimental programs and global QCD analyses.