In recent decades, mixed-criticality systems have been widely adopted to reduce the complexity and development times of real-time critical applications. In these systems, applications run on a separation kernel hypervisor, a software element that controls the execution of the different operating systems, providing a virtualized environment and ensuring the necessary spatial and temporal isolation. The guest code can run unmodified and unaware of the hypervisor or be explicitly modified to have a tight coupling with the hypervisor. The former is known as full virtualization, while the latter is known as para-virtualization. Full virtualization offers better compatibility and flexibility than para-virtualization at the cost of a performance penalty. LEON is a processor family that implements the SPARC V8 architecture and whose use is widespread in the field of space systems. To the best of our knowledge, all separation kernel hypervisors designed to support the development of mixed-criticality systems for LEON employ para-virtualization, which hinders the adaptation of real-time operating systems. This article presents the design of a Virtualization Monitor that allows guest real-time operating systems to run virtualized on LEON-based systems without needing to modify their source code. It is designed as a stand-alone component within a hypervisor and incorporates a set of techniques such as static binary rewriting, automatic code generation, and the use of operating system profiles. To validate the proposed solution, tests and benchmarks have been implemented for three guest systems, RTEMS, FreeRTOS, and Zephyr, analyzing the overhead introduced in certain situations characteristic of real-time applications. Finally, the same benchmarks have been run on AIR, one of the hypervisors that uses para-virtualization. The results obtained show that the use of the proposed techniques allows us to obtain similar results to those obtained using para-virtualization without the need to modify the source code of the guest real-time operating systems.