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Time-sensitive data acquisition is critical for many Low-Power Wide-Area Network (LPWAN) applications, such as healthcare monitoring and industrial Internet of Things. Among the available LPWAN technologies, LoRa (Long Range) has emerged as a leading choice, offering kilometer-scale communication with minimal power consumption and enabling high-density deployments across large areas. However, the conventional ALOHA-based Medium Access Control (MAC) in LoRa is not designed to support real-time communication over large-scale networks. This paper introduces LoRaHART, a novel approach that overcomes two critical, under-explored limitations in Commercial Off The Shelf (COTS) LoRa gateways that impact real-time performance. LoRa gateways have limited capacity for demodulation of parallel transmissions and their antenna can either transmit or receive at any time instant. LoRaHART incorporates a hardware-aware super-frame structure, comprising both Time Division Multiple Access (TDMA) slots as well as opportunistic retransmissions using Carrier Sense Multiple Access (CSMA), designed to mitigate the above constraints. We use a partial packing and makespan minimization algorithm to schedule periodic real-time transmissions efficiently within the TDMA slots, and also develop a probabilistic node contention model for CSMA retransmissions, providing analytical guarantees for deadline satisfaction under ideal channel conditions. Our evaluation of LoRaHART on a 40-node LoRa testbed demonstrates significant improvements over existing solutions in practice, achieving an average Packet Reception Ratio of 98% and a 45% higher airtime utilization than the best performing baseline.