Mobile devices offload latency-sensitive application tasks to edge servers to satisfy applications' Quality of Service (QoS) deadlines. Consequently, ensuring reliable offloading without QoS violations is challenging in distributed and unreliable edge environments with diverse resource and reliability levels. We propose FRESCO, a fast and reliable edge offloading framework that utilizes a blockchain-based reputation system, which enhances the reliability of offloading in the distributed edge. The distributed reputation system tracks the historical performance of edge servers, while blockchain through a consensus mechanism ensures that sensitive reputation information is secured against tampering. However, blockchain consensus typically has high latency, and therefore we employ a Hybrid Smart Contract (HSC) as areputation state managerthat automatically computes and stores reputation securely on-chain (i.e., on the blockchain) while allowing fast offloading decisions off-chain (i.e., outside of blockchain). Theoffloading decision engineuses a reputation score from HSC to derive fast offloading decisions, which are based on Satisfiability Modulo Theory (SMT). The SMT can formally guarantee a feasible solution that is valuable for latency-sensitive applications that require high reliability. With a combination of an on-chain HSC reputation state manager and an off-chain SMT decision engine, FRESCO offloads tasks to reliable servers without being hindered by blockchain consensus. In our experiment, FRESCO reduces response time by up to 7.86 times and saves energy by up to 5.4% compared to all baselines while minimizing QoS violations to 0.4% and achieving an average decision time of just 5.05 milliseconds.