Inertial sensors continuously track the 3D orientation of a flying drone, serving as the bedrock for maneuvers and stabilization. However, even the best inertial measurement units (IMU) are prone to various types of correlated failures. We consider using multiple GPS receivers on the drone as a failsafe mechanism for IMU failures. The core challenge is in accurately computing the relative locations between each receiver pair, and translating these measurements into the drone's 3D orientation. Achieving IMU-like orientation requires the relative GPS distances to be accurate to a few centimeters - a difficult task given that GPS today is only accurate to around 1-4 meters. Moreover, GPS-based orientation needs to be precise even under sharp drone maneuvers, GPS signal blockage, and sudden bouts of missing data. This paper designs SafetyNet, an off-the-shelf GPS-only system that addresses these challenges through a series of techniques, culminating in a novel particle filter framework running over multi-GNSS systems (GPS, GLONASS, and SBAS). Results from 11 sessions of 5-7 minute flights report median orientation accuracies of 2° even under overcast weather conditions. Of course, these improvements arise from an increase in cost due to the multiple GPS receivers, however, when safety is of interest, we believe that tradeoff is worthwhile.