Arbitrary point-to-point (P2P) routing is becoming a necessity in a multitude of Internet-of-Things (IoT) applications, including building automation, smart cities, and smart manufacturing. For this reason, new P2P routing protocols such as lightweight on-demand ad hoc distance-vector routing protocol next generation (LOADng) and ad hoc on-demand distance vector routing-based RPL protocol (AODV-RPL) are being standardized. Both protocols are inspired by AODV, and hence, they might suffer from broadcast storms caused by flooding route requests (RREQs) and related issues. Thus, while AODV-RPL takes advantage of RPL mechanisms, LOADng uses blind flooding to forward RREQs. However, both lack effective techniques for avoiding unnecessary RREQ transmissions when routes are found. In this article, we first deploy stopping Trickle timers to ensure scalable, efficient, and reliable dissemination of RREQs. Second, we devise and present new techniques to suppress unnecessary RREQs with optimizations for radio duty-cycled networks. Finally, the two mechanisms are combined in a third proposal for better efficiency. These mechanisms provide individually and collectively great enhancements to P2P routing protocols, such as AODV-RPL and LOADng, while staying backward compatible with their base specifications. The performance of the proposed mechanisms when applied to LOADng has been validated using both extensive time-accurate simulations and large-scale public testbeds. The obtained results have shown the effectiveness of the proposed mechanisms with around 50% less overhead and savings in energy consumption, along with a 20% gain in route discovery ratio at the expense of an increase in discovery delays.