Wireless sensor networks are characterized by low power consumption because motes are typically battery-powered. Time slotted channel hopping (TSCH) relies on a fixed transmission schedule, which enables the receiver module of wireless motes to be switched off every time it is not needed. Unfortunately, in many practical contexts most of the reserved slots remain unused, which leads to appreciable energy waste. For periodic traffic, proactive reduction of idle listening (PRIL) techniques have been proven able to mitigate this problem.In this paper, PRIL multi-hop (PRIL-M) is introduced with the aim to improve existing PRIL techniques, by lowering energy waste further in large real-world mesh networks. PRIL-M is advantageous in all those contexts where ultra-low power consumption is more important than end-to-end latency. Applications that can benefit from PRIL-M include, e.g., environmental monitoring, where sensors are deployed over the target area and must operate for years without maintenance. A thorough simulation campaign showed that, in these scenarios, energy consumption of PRIL-M is 75% less than standard TSCH, while the average latency is about 20 times larger.