In a decade, AI frontier research transitioned from the researcher's workstation to thousands of high-end hardware-accelerated compute nodes. This rapid evolution shows no signs of slowing down in the foreseeable future. While top cloud providers may be able to keep pace with this growth rate, obtaining and efficiently exploiting computing resources at that scale is a daunting challenge for universities and SMEs. This work introduces the Cross-Facility Federated Learning (XFFL) framework to bridge this compute divide, extending the opportunity to efficiently exploit multiple independent data centres for extreme-scale deep learning tasks to data scientists and domain experts. XFFL relies on hybrid workflow abstractions to decouple tasks from environment-specific technicalities, reducing complexity and enhancing reusability. In addition, Federated Learning (FL) algorithms eliminate the need to move large amounts of data between different facilities, reducing time-to-solution and preserving data privacy. The XFFL approach is empirically evaluated by training a full LLaMAv2 7B instance on two facilities of the EuroHPC JU, showing how the increased computing power completely compensates for the additional overhead introduced by two data centres.