Low Earth Orbit (LEO) satellites have been widely used to collect sensing data from ground-based IoT devices. Comprehensive and timely collection of sensor data is a prerequisite for conducting analysis, decision-making, and other tasks, ultimately enhancing services such as geological hazard monitoring and ecological environment monitoring. To improve the efficiency of data collection, many models and scheduling methods have been proposed, but they did not fully consider the practical scenarios of collecting data from remote areas with limited ground network coverage, particularly in addressing the uncertainties in data transmission caused by complex environments. To cope with the above challenges, this paper first presents a mathematical representation of the real-world scenario for data collection from geographically distributed IoT devices through LEO satellites, based on a full consideration of uncertainties in transmission rates. Then, a Cross-entropy-based transmission scheduling method (CETSM) and an uncertainty-aware transmission scheduling method (UATSM) are proposed to enhance the volume of collected data and mitigate the impact of uncertainty on the data uplink transmission rate. The CETSM achieved an average increase in total data collection ranging from 7.24% to 16.69% compared to the other five benchmark methods across eight scenarios. Moreover, UATSM performs excellently in the Monte Carlo-based evaluation module, achieving an average data collection completion rate of 96.1% and saving an average of 19.8% in energy costs, thereby obtaining a good balance between energy consumption and completion rate.