To support mission-critical services in emergency scenarios, wireless networks are required to provide stringent guarantees under massive Ultra-Reliable Low-Latency Communications (mURLLC) constraints. Distributed unmanned aerial vehicle (UAV)-based massive multiple-input multiple-output (MIMO) architectures have recently emerged as a promising solution for rapidly deployable emergency communication systems. However, how to fundamentally characterize and guarantee statistical quality-of-service (QoS) for such systems in the finite blocklength regime remains largely unexplored. To overcome these challenges, in this paper we develop a fundamental analytical framework for delay and reliability bounded QoS guarantees in distributed UAV-based massive MIMO emergency networks under finite blocklength coding (FBC). By rigorously modeling the stochastic service process of distributed massive MIMO fading channels, we derive statistical characterizations the delay and error-rate bounded QoS exponents. We also establish QoS-driven controlling functions, including the $ε$-effective capacity and the feasible QoS region. Finally, the obtained simulation results validate and evaluate our developed modeling techniques and asymptotic formulations to support mURLLC.