Long gamma-ray burst's (LGRB's) association with the death of massive stars suggests that they could be used to probe the cosmic star formation history (CSFH) with high accuracy, due to their high luminosities. We utilize cosmological simulations from the First Billion Years project to investigate the biases between the CSFH and the LGRB rate at z > 5, assuming various different models and constraints on the progenitors of LGRBs. We populate LGRBs using a selection based on environmental properties and demonstrate that the LGRB rate should trace the CSFH to high redshifts. The measured LGRB rate suggests that LGRBs have opening angles of θjet = 0.1°, although the degeneracy with the progenitor model cannot rule out an underlying bias. We demonstrate that proxies that relate the LGRB rate with global LGRB host properties do not reflect the underlying LGRB environment, and are in fact a result of the host galaxy's spatial properties, such that LGRBs can exist in galaxies of solar metallicity. However, we find a class of host galaxies that have low stellar mass and are metal rich, and that their metallicity dispersions would not allow low-metallicity environments. Detection of hosts with this set of properties would directly reflect the progenitor's environment. We predict that 10 per cent of LGRBs per year are associated with this set of galaxies that would have forbidden line emission that could be detected by instruments on the James Webb Space Telescope. Such a discovery would place strong constraints on the collapsar model and suggests other avenues to be investigated.