The virtual integration of geographically distributed Research Infrastructures (RIs) for joint experiments in the domain of power and energy systems poses numerous challenges, particularly in terms of tool compatibility and user-friendliness. To address some of these challenges, this work presents the development and implementation of a laboratory-based middleware and data exchange service as part of the H2020 ERIGrid 2.0 project. The middleware comprises a suite of shared software tools and services designed to seamlessly integrate RIs including transport protocols as well as interface semantics. Specifically, this work details the development of a simplified and standardised interface known as the Universal Application Programming Interface (UAPI). It eliminates the need for users to grapple with the diverse intricacies of each individual RI, offering instead a tool-agnostic and standardised interface for conducting joint experiments. The work also presents and discusses the results of a real-world case study of a geographically distributed, sector-coupling experiment conducted between laboratories in Denmark, Greece, Italy, Netherlands, and Norway utilising the developed middleware.