Sub-Saharan Africa hosts more than 570 million people without reliable access to electricity, with rural communities in mountainous terrain — such as Rwanda's Eastern Province — facing prohibitive grid-extension economics that average above 8,500 USD per kilometre of medium-voltage line. While solar photovoltaic (PV) systems coupled with lithium-ion battery storage have become the de-facto standard for off-grid electrification, battery-only architectures suffer from severe seasonal mismatch in equatorial climates where the long rainy season (March–May) produces 4–7 consecutive low-irradiance days that exceed the practical economic sizing of electrochemical storage. This paper presents the design, simulation and field validation of a hybrid solar–hydrogen microgrid that combines a 50 kWp PV array, an 8 kW Proton Exchange Membrane (PEM) electrolyzer, a 50 Nm³ compressed hydrogen tank, a 5 kW PEM fuel cell, and a 100 kWh lithium-iron-phosphate (LFP) battery, all coordinated by an adaptive Energy Management System (EMS) implemented on an STM32 micro-controller. The system was deployed at a 240-household village in Kayonza District, Rwanda, and benchmarked against five alternative configurations over a 20-year project lifecycle. Field measurements during the May 2025 monsoon period confirmed a Loss of Power Supply Probability (LPSP) of 0.6 %, a renewable energy fraction of 96 %, and a Levelised Cost of Electricity (LCOE) of 0.17 USD/kWh — a 32 % reduction relative to the best PV-battery configuration and a 60 % reduction relative to grid extension.