Due to the geographic distribution of its subscribers, Ethernet Passive Optical Networks (EPONs) have typically varying propagation delays between the Optical Network Units (ONUs) and the Optical Line Terminal (OLT). In this paper, we consider EPONs with an offline scheduling framework, which enables Quality-of-Service mechanisms by collecting bandwidth requests from all ONUs before the OLT makes dynamic bandwidth allocations for transmissions on the shared ONUs-to- OLT upstream channel. We propose and evaluate the Shortest Propagation Delay (SPD) first scheduling policy which sequences the ONUs' upstream transmissions in increasing order of the ONUs' propagation delays, i.e., the upstream transmission of the ONU with the smallest propagation delay is scheduled first. We formally analyze the competitiveness of SPD first scheduling and find that it achieves very close to optimal performance. We characterize the stability limit for Gated and Limited grant sizing in conjunction with SPD grant scheduling. We evaluate the cycle length and packet delay with SPD scheduling through probabilistic analysis and simulations and find significant reductions in packet delay with SPD first scheduling in EPONs with heterogeneous propagation delays, especially when Limited grant sizing is employed.