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We assess the variance of the post-collapse evolution remnants of compact, massive, low-metallicity stars, under small changes in the degrees of rotation and magnetic field of selected pre-supernova cores. These stellar models are commonly considered progenitors of long gamma-ray bursts. The fate of the proto-neutron star (PNS) formed after collapse, whose mass may continuously grow due to accretion, critically depends on the poloidal magnetic field strength at bounce. Should the poloidal magnetic field be sufficiently weak, the PNS collapses to a black hole (BH) within a few seconds. Models on this evolutionary track contain promising collapsar engines. Poloidal magnetic fields smooth over large radial scales (e.g. dipolar fields) or slightly augmented with respect to the original pre-supernova core yield long-lasting PNSs. In these models, BH formation is avoided or staved off for a long time, hence, they may produce proto-magnetars (PMs). Some of our PM candidates have been run for $\lesssim 10\,$s after core bounce, but they have not entered the Kelvin-Helmholtz phase yet. Among these models, some display episodic events of spin-down during which we find properties broadly compatible with the theoretical expectations for PMs ($M_{PNS} \approx 1.85\,M_\odot - 2.5\,M_\odot$, $\bar{P}_{PNS} \approx 1.5 - 4\,$ms, and $b^{\rm surf}_{PNS} \lesssim 10^{15}\,$G) and their very collimated supernova ejecta has nearly reached the stellar surface with (still growing) explosion energies $\gtrsim 2\times 10^{51}\,$erg.