We analyze the properties of 42 rapidly rotating, low-metallicity, quasi-chemically homogeneously evolving stellar models in the mass range between 4 and 45, M at the time of core collapse. Such models were proposed as progenitors for both superluminous supernovae (SLSNe) and long-duration gamma-ray bursts (lGRBs) and the Type Ic-BL supernovae (SNe) that are associated with them. Our findings suggest that whether these models produce a magnetar-driven SLSN explosion or a near-critically rotating black hole is not a monotonic function of the initial mass. Rather, their explodability varies nonmonotonically depending on the late core evolution, once chemical homogeneity is broken. Using different explodability criteria, we find that our models have a clear preference to produce SLSNe at lower masses and lGRBs at higher masses, but we find several exceptions, expecting lGRBs to form from stars as low as 10 M and SLSNe with progenitors as massive as 30 M. In general, our models reproduce the predicted angular momenta, ejecta masses, and magnetic field strengths at core collapse inferred for SLSNe and lGRBs and suggest significant interaction with their circumstellar medium, particularly for explosions with low ejecta mass.