In one embodiment, a method comprises: generating, by a constrained low power and lossy network (LLN) device that is localized within a subregion of an LLN, a thin destination oriented directed acyclic graph (DODAG) having up to a prescribed limit of attached LLN devices at each hop of the thin DODAG based on generating a DODAG information object (DIO) message specifying an instruction for limiting attachment at each hop of the thin DODAG to the prescribed limit; and causing, by the constrained LLN device, multicast-only transmissions via the thin DODAG based on inserting into the DIO message a multicast-only transmission mode via the thin DODAG and outputting the DIO message, the DIO message causing each neighboring LLN device to selectively attach to the constrained LLN device as an attached child LLN device based on the instruction and execute the multicast-only transmissions via the thin DODAG.