Unmanned Aerial Vehicles (UAVs), or drones, are increasingly expected to operate in spaces populated by humans while avoiding injury to people or damaging property. However, incidents and accidents can, and increasingly do, happen. Traditional investigations of aircraft incidents require on-board flight data recorders (FDRs); however, these physical FDRs only work if the drone can be recovered. A further complication is that physical FDRs are too heavy to mount on light drones, hence not suitable for forensic digital investigations of drone flights. In this paper, we propose a self-adaptive software architecture, LiveBox, to make drones both forensic-ready and regulation compliant. We studied the feasibility of using distributed technologies for implementing the LiveBox reference architecture. In particular, we found that updates and queries of drone flight data and constraints can be treated as transactions using decentralised ledger technology (DLT), rather than a generic time-series database, to satisfy forensic tamper-proof requirements. However, DLTs such as Ethereum, have limits on throughput (i.e. transactions-per-second), making it harder to achieve regulation-compliance at runtime. To overcome this limitation, we present a self-adaptive reporting algorithm to dynamically reduce the precision of flight data without sacrificing the accuracy of runtime verification. Using a real-life scenario of drone delivery, we show that our proposed algorithm achieves a 46% reduction in bandwidth without losing accuracy in satisfying both tamper-proof and regulation-compliant requirements.