With the scope of Industry 4.0 and the Industrial Internet of Things (IIoT), wireless technologies have gained momentum in the industrial realm. Wireless standards such as WirelessHART, ISA100.11a, IEEE 802.15.4e and 6TiSCH are among the most popular, given their suitability to support real-time data traffic in wireless sensor and actuator networks (WSAN). Theoretical and empirical studies have covered prioritized packet scheduling in extenso, but only little has been done concerning methods that enhance and/or guarantee real-time performance based on routing decisions. In this work, we propose a greedy heuristic to reduce overlap in shortest-path routing for WSANs with packet transmissions scheduled under the earliest-deadline-first (EDF) policy. We evaluated our approach under varying network configurations and observed remarkable dominance in terms of the number of overlaps, transmission conflicts, and schedulability, regardless of the network workload and connectivity. We further observe that well-known graph network parameters, e.g., vertex degree, density, betweenness centrality, etc., have a special influence on the path overlaps, and thus provide useful insights to improve the real-time performance of the network.