Performing accurate simulations of large- and multi-scale electromagnetics problems has far-reaching implications in a variety of engineering and scientific disciplines. The same physics governs a diversity of applications including problems of importance for the 5G and automotive communications industries such as complex radome-antenna and antenna-vehicle interactions. Antenna performance characterization is an increasingly important task for users as the number and complexity of antenna systems grows. Simulations are currently suboptimal in the sense that they either lack the required fidelity or simply cannot be executed within the computational and financial resource constraints. Such simulation problems involve complex materials, multiple feeds and loads, multiscale meshing challenges, and geometries that may exceed 1000 wavelengths in one or more dimensions. Recent work has shown the potential benefit of using high-order basis functions (HOBF) for rapidly reducing simulation error with great efficiency per degree-of-freedom (DoF). However, use of HOBF requires an attendant use of high-order geometry (HOG) so that the underlying model is represented appropriately for the desired simulation accuracy motivating use of HOBF. In this work, the authors present a combination of improvements to the state-of-the-art for implementation of HOBF with HOG at production-grade maturity. Numerous demonstrations are shown including complex antenna-radome interactions involving radomes with multiple thin layers. For many classes of electrically large scattering and antenna problems, the combination of HOBF and HOG is simply not enough to enable solution on available computational resources. To support ever-larger simulations, the authors have developed a combination of HOBF with novel matrix compression techniques, which preserve high-order convergence while still supporting high levels of matrix compression. Further, the authors have implemented these compression techniques in a distributed computing environment. Demonstration of a large-scale reflector model is shown with a comparison of the benefits of HOBF compression applied versus a traditional point-wise distributed solution.