The exponential growth of Internet of Things (IoT) applications led to the deployment of IoT devices in remote areas beyond the reach of terrestrial networks, calling for satellite network solutions. Indeed, Low-Earth Orbit (LEO) satellites can provide global connectivity to direct-to-satellite (DtS)-IoT applications, with remarkable impact in several areas, as environmental monitoring, precision agriculture, and disaster prevention. One of the key challenges in DtS-IoT is supporting energy and spectral efficient multiple access, which has attracted a lot of attention recently. This work presents two novel multiple-access scheduling strategies for DtS-IoT networks, both inspired by the scheduling algorithm for LoRa to LEO satellites (SALSA). The latter prevents collisions by applying a first-come-first-served (FCFS) policy to allocate dedicated time slots according to the devices' rise times. However, the effectiveness of SALSA decreases in high-density scenarios, for which the visibility time of many devices is insufficient to successfully schedule their transmission. In the proposed scheduling methods, we take advantage of the availability of multiple frequency channels and the ability to change the transmission scheduling order of some devices within a visibility time window to improve uplink efficiency. The numerical results show that the average number of uplinks per lap and per visible device increases with the number of available channels, providing an improvement of almost 80% in terms of system uplink efficiency, and the proposed scheduling methods are more effective with smaller packet sizes. Additionally, we explore that the fusion of both scheduling strategies can further boost the system performance while guaranteeing an uplink efficiency greater than 50%, as elucidated across the implementation algorithms with four, six, and eight multiple channels.