High-performance computing (HPC) is a major driver accelerating scientific research and discovery, from quantum simulations to medical therapeutics. The growing number of new HPC systems coming online are being furnished with various hardware components, engineered by competing industry entities, each having their own architectures and platforms to be supported. While the increasing availability of these resources is in many cases pivotal to successful science, even the largest collaborations lack the computational expertise required for maximal exploitation of current hardware capabilities. The need to maintain multiple platform-specific codebases further complicates matters, potentially adding a constraint on the number of machines that can be utilized. Fortunately, numerous programming models are under development that aim to facilitate software solutions for heterogeneous computing. In this paper, we leverage the SYCL programming model to demonstrate cross-platform performance portability across heterogeneous resources. We detail our NVIDIA and AMD random number generator extensions to the oneMKL open-source interfaces library. Performance portability is measured relative to platform-specific baseline applications executed on four major hardware platforms using two different compilers supporting SYCL. The utility of our extensions are exemplified in a real-world setting via a high-energy physics simulation application. We show the performance of implementations that capitalize on SYCL interoperability are at par with native implementations, attesting to the cross-platform performance portability of a SYCL-based approach to scientific codes.