The Internet of Things (IoT) connects a plethora of smart devices globally across various applications like smart cities, autonomous vehicles, and health monitoring. Simulation plays a key role in the testing of IoT systems, noting that field testing of a complete IoT product may be infeasible or prohibitively expensive. This paper addresses a specific yet important need in simulation-based testing for IoT: Stress testing of cloud systems that are increasingly employed in IoT applications. Existing stress testing solutions for IoT demand significant computational resources, making them ill-suited and costly. We propose a lean simulation framework designed for IoT cloud stress testing. The framework enables efficient simulation of a large array of IoT and edge devices that communicate with the cloud. To facilitate simulation construction for practitioners, we develop adomain-specific language (DSL), named IoTECS, for generating simulators from model-based specifications. We provide the syntax and semantics of IoTECS and implement IoTECS using Xtext and Xtend. We assess simulators generated from IoTECS specifications for stress testing two real-world systems: a cloud-based IoT monitoring system developed by our industry partner and an IoT-connected vehicle system. Our empirical results indicate that simulators created using IoTECS: (1) achieve best performance when configured with Docker containerization; (2) effectively assess the service capacity of our case-study systems, and (3) outperform industrial stress-testing baseline tools, JMeter and Locust, by a factor of 3.5 in terms of the number of IoT and edge devices they can simulate using identical hardware resources. To gain initial insights about the usefulness of IoTECS in practice, we interviewed two engineers from our industry partner who have firsthand experience with IoTECS. Feedback from these interviews suggests that IoTECS is effective in stress testing IoT cloud systems, saving significant time and effort.