Off-grid PV systems have been proposed as a panacea for economies with poor electricity access, offering a lower-cost “leapfrog” over grid infrastructure used in higher-income economies. However, reliability and carbon pricing impacts have been omitted from work that examines pathways to electricity access, underplaying the potential of off-grid PV. We perform high-resolution geospatial analysis on universal household electricity access in Sub-Saharan Africa that includes these aspects via least-cost pathways at different electricity demand levels. Under our "Tier 3" demand reference scenario, 24% of our study’s 470 million people obtaining electricity access by 2030 do so via off-grid PV. A penalty for unmet demand (0.50 $/kWh) increases this share to 41% and applying a carbon price (around $80/tonne CO2-eq) increases it to 38%. We identify thresholds for policy effectiveness in different regions and highlight the high degree of spatial heterogeneity and the areas where policy intervention may be most effective.