Current tablet-based interfaces for drone operations often impose a heavy cognitive load on pilots and reduce situational awareness by dividing attention between the video feed and the real world. To address these challenges, we designed a heads-up augmented reality (AR) interface that overlays in-situ information to support drone pilots in safety-critical tasks. Through participatory design workshops with professional pilots, we identified key features and developed an adaptive AR interface that dynamically switches between task and safety views to prevent information overload. We evaluated our prototype by creating a realistic building inspection task and comparing three interfaces: a 2D tablet, a static AR, and our adaptive AR design. A user study with 15 participants showed that the AR interface improved access to safety information, while the adaptive AR interface reduced cognitive load and enhanced situational awareness without compromising task performance. We offer design insights for developing safety-first heads-up AR interfaces.