Multi-hop wireless networks with autonomous nodes are susceptible to selfish traffic remapping attacks (TRAs). Nodes launching TRAs leverage the underlying channel access function to receive an unduly high quality of service (QoS) for packet flows traversing source-to-destination routes. TRAs are easy to execute, impossible to prevent, difficult to detect, and harmful to the QoS of honest nodes. Recognizing the need for providing QoS security, we use a novel network-oriented QoS metric to propose a self-enforcing game-theoretic mitigation approach. By switching between TRA and honest behavior, selfish nodes engage in a noncooperative multistage game in pursuit of high QoS. We analyze feasible node strategies and design a distributed signaling mechanism called DISTRESS, under which, given certain conditions, the game produces a desirable outcome: after an upper-bounded play time, honesty tends to become a selfish node's best reply behavior, while yielding acceptable QoS to most or all nodes. We verify these findings by Monte Carlo and ns-3 simulations of static and mobile nodes.