In one embodiment, a node may determine a trigger for establishing transmission priority on a path through a shared-media communication network for priority traffic to a particular node. As such, the node may generate a path clear message (PCM) that would instruct one or more receiving nodes along the path to suspend transmission for traffic other than the priority traffic for a specified duration, and also to transmit a local non-repeated distributed message to one or more neighbor nodes of each respective receiving node, the local non-repeated distributed message to instruct the neighbor nodes to suspend transmission for the specified duration. After transmitting the PCM along the path to the particular node to establish the transmission priority for the priority traffic along the path through the shared-media network, the priority traffic may be transmitted to the particular node along the path during the transmission priority.