An effective way to increase the timing predictability of multicore platforms is to use nonpreemptive scheduling. It reduces preemption and job migration overheads, avoids intra-core cache interference, and improves the accuracy of worst-case execution time (WCET) estimates. However, existing schedulability tests for global non-preemptive multiprocessor scheduling are pessimistic, especially when applied to periodic workloads. This paper reduces this pessimism by introducing a new type of sufficient schedulability analysis that is based on an exploration of the space of possible schedules using concise abstractions and state-pruning techniques. Specifically, we analyze the schedulability of non-preemptive job sets (with bounded release jitter and execution time variation) scheduled by a global job-level fixed-priority (JLFP) scheduling algorithm upon an identical multicore platform. The analysis yields a lower bound on the best-case response-time (BCRT) and an upper bound on the worst-case response time (WCRT) of the jobs. In an empirical evaluation with randomly generated workloads, we show that the method scales to 30 tasks, a hundred thousand jobs (per hyperperiod), and up to 9 cores.