In one embodiment, a method comprises attaching, by a constrained network device in a data network, to a first parent network device in a tree-based storing mode topology in response to receiving a first advertisement message generated by the first parent network device; outputting to the first parent network device a plurality of routes stored in the constrained network device, the routes identifying destinations reachable via the constrained network device; determining, by the constrained network device, that the first parent network device is encountering saturation of stored routes based on the constrained network device receiving a second advertisement message from the first parent network device; and eliminating, by the constrained network device, the saturation encountered by the first parent network device based on moving at least a portion of the routes from the first parent network device to a second parent network device in the tree-based storing mode topology.