In one embodiment, a method comprises: joining, by a network device, a network topology rooted by a root network device in a data network, and in response transmitting an advertisement indicating a position of the network device in the network topology; suppressing a second transmission based on initiating a deferred transmission operation in response to transmitting the advertisement; maintaining the deferred transmission operation to enable a prescribed minimum number of other network devices to join the network topology at respective identified lower positions than the position of the network device; and changing, by the network device, from the deferred transmission operation to an accelerated operation in response to expiration of a prescribed deferral interval or detecting the prescribed minimum number of other network devices having the respective identified lower positions, the accelerated operation enabling the network device to initiate transmission of a data packet before the other network devices.