In disaster response and other infrastructure-limited settings, UAV-mounted access points can rapidly restore service availability for mobile ground users as demand and fleet availability evolve. Existing single-slot coverage formulations, however, can mask prolonged individual outages and do not jointly represent heterogeneous service priorities, finite battery capacities, and periodic recharging. We study persistent geometricmulti-UAV service coverage, where a user is available for service when it lies inside a UAV footprint. We propose Priority- and Outage-Guided Safe QMIX (POGS-QMIX), a hybrid hierarchical framework in which a centralized online coordinator forms conflict-reduced UAV–user targets from fleet-wide priority and outage information, while parameter-shared QMIX agents independently choose target-conditioned low-level actions. The framework couples class-balanced outage memory, assignment, dense target-progress feedback, and a return-energy action mask. The evaluation includes learning and non-learning baselines, greedy-versus-Hungarian assignment, multi-seed statistics, sensitivity studies, operating-condition studies, and energy-stress tests. In the default scenario, POGS-QMIX obtains high-priority coverage $0.547\pm 0.009$ and maximum high-priority outage $38.0\pm 4.7$ slots over five independent seeds.