Spatially partitioned heterogeneous accelerators (HAs) are increasingly adopted in embedded systems for their performance and flexibility. Yet most existing HA design frameworks optimize primarily for throughput or quality-of-service (QoS) metrics. They often overlook safety-critical real-time requirements, including hardware support for predictable execution, real-time-aware design space exploration (DSE), and rigorous schedulability analysis. These requirements are essential in safety-critical applications such as smart transportation, where schedulability guarantees directly affect system safety. To address this gap, we present PHAROS, a real-time-centric HA design framework. PHAROS introduces preemption mechanisms and scheduler designs for spatially partitioned HAs under first-in-first-out (FIFO) and earliest-deadline-first (EDF) policies. Leveraging modern real-time theory, we further develop a soft real-time (SRT) schedulability-oriented DSE with objectives and constraints tailored to SRT schedulability. Through comprehensive modeling, analysis, and evaluation across diverse applications, we show that PHAROS’s schedulability-oriented DSE discovers more feasible configurations for a broader range of task sets than throughput-oriented DSE baselines, while delivering improved real-time performance. We also provide response-time analyses for the supported scheduling algorithms.