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Although the idea of using wireless links for covering large areas is not new, the advent of LPWANs has recently started changing the game. Simple, robust, narrowband modulation schemes permit the implementation of low-cost radio devices offering high receiver sensitivity, thus improving the overall link budget. The several technologies belonging to the LPWAN family, including the well-known LoRaWAN solution, provide a cost-effective answer to many Internet-of-things (IoT) applications, requiring wireless communication capable of supporting large networks of many devices (e.g., smart metering). Generally, the adopted MAC strategy is based on pure ALOHA, which, among other things, allows to minimize the traffic overhead under constrained duty cycle limitations of the unlicensed bands. Unfortunately, ALOHA suffers from poor scalability, rapidly collapsing in dense networks. This work investigates the design of an improved LoRaWAN MAC scheme based on slotted ALOHA. In particular, the required time dissemination is provided by out-of-band communications leveraging on FM-RDS broadcasting. An experimental setup based on low-cost hardware is used to characterize the obtainable synchronization performance and derive a timing error model. Consequently, improvements in success probability and energy efficiency have been validated by means of simulations in very large networks with up to 10000 nodes. It is shown that the advantage of the proposed scheme over conventional LoRaWAN communication is up to 100% when short update time and large payload are required. Similar results are obtained regarding the energy efficiency improvement, which is close to 100% for relatively short transmission intervals and long message duration; however, due to the additional overhead for listening to the time dissemination messages, efficiency gain can be negative for short-duration messages fastly repeating.