Uncertainty Quantification (UQ) workloads are becoming increasingly common in science and engineering. They involve the submission of thousands or even millions of similar tasks with potentially unpredictable runtimes, where the total number is usually not known a priori. A static one-size-fits-all batch script would likely lead to suboptimal scheduling, and native schedulers installed on High Performance Computing (HPC) systems such as SLURM often struggle to efficiently handle such workloads. In this paper, we introduce a new load balancing approach suitable for UQ workflows. To demonstrate its efficiency in a real-world setting, we focus on the GS2 gyrokinetic plasma turbulence simulator. Individual simulations can be computationally demanding, with runtimes varying significantly-from minutes to hours-depending on the high-dimensional input parameters. Our approach uses UQ and Modelling Bridge, which offers a language-agnostic interface to a simulation model, combined with HyperQueue which works alongside the native scheduler. In particular, deploying this framework on HPC systems does not require system-level changes. We benchmark our proposed framework against a standalone SLURM approach using GS2 and a Gaussian Process surrogate thereof. Our results demonstrate a reduction in scheduling overhead by up to three orders of magnitude and a maximum reduction of 38% in CPU time for long-running simulations compared to the naive SLURM approach, while making no assumptions about the job submission patterns inherent to UQ workflows.