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In this work, we investigate an alternative channel for the formation of fast-spinning black hole–neutron star (BHNS) binaries, in which super-Eddington accretion is expected to occur in accreting BHs during the stable mass transfer phase within BH-stripped helium (BH–He-rich) star binary systems. We evolve intensive MESA grids of close-orbit BH–He-rich star systems to systematically explore the projected aligned spins of BHs in BHNS binaries, as well as the impact of different accretion limits on the tidal disruption probability and electromagnetic (EM) signature of BHNS mergers. Most of the BHs in BHNS mergers cannot be effectively spun up through accretion if the accretion rate is limited to $\lesssim 10\,{\dot{M}}_{\mathrm{Edd}}$ , where ${\dot{M}}_{\mathrm{Edd}}$ is the standard Eddington accretion limit. In order to reach high spins (e.g., χ _BH ≳ 0.5), the BHs are required to be born less massive (e.g., ≲3.0 M _⊙ ) in binary systems with initial periods of ≲0.2–0.3 days and accrete material at $\sim 100\,{\dot{M}}_{\mathrm{Edd}}$ . However, even under this high accretion limit, ≳6 M _⊙ BHs are typically challenging to significantly spin up and generate detectable associated EM signals. Our population simulations suggest that different accretion limits have a slight impact on the ratio of tidal disruption events. However, as the accretion limit increases, the EM counterparts from the cosmological BHNS population can become bright overall.