We consider global fixed-priority (G-FP) scheduling of parallel tasks, in which each task is represented as a directed acyclic graph (DAG). We summarize and highlight limitations of the state-of-the-art analyses for G-FP and propose a novel technique for bounding interfering workload, which can be applied directly to generalized DAG tasks. Our technique works by constructing optimization problems for which the optimal solution values serve as safe and tight upper bounds for interfering workloads. Using the proposed workload bounding technique, we derive a response-time analysis and show that it improves upon state-of-the-art analysis techniques for G-FP scheduling.