Rydberg atoms exhibit exceptional sensitivity to long-wave electric fields, presenting a promising solution to the signal degradation that plagues ground-based long-wave time-service systems in remote or weak-signal regions. However, practical Loran-C signal reception using Rydberg-atom sensors is currently limited by fidelity deterioration, primarily caused by electrostatic shielding from vapor cell walls and frequency-doubling noise. In this work, we prepare Rydberg atoms via a two-photon excitation scheme and integrate them with a modulation transfer spectroscopy (MTS) and electromagnetically induced transparency (EIT) frequency-stabilization system. By employing a parallel-plate vapor cell subjected to a strong DC bias field, we leverage the DC Stark effect to precisely modulate the EIT resonance frequency shift, thereby overcoming the aforementioned limitations. This approach enables high-fidelity reception of Loran-C signals, accompanied by comprehensive time- and frequency-domain analyses. Quantitative measurements demonstrate a single-pulse fidelity of 98.0% and an envelope cycle difference (ECD) of 0.08 μs. Furthermore, by extracting and comparing the phase-reversal characteristics of odd- and even-period pulse trains, we rigorously verify the phase stability of the Rydberg-atom antenna. This work provides a robust technical foundation for the reception and demodulation of long-wave time-service signals using Rydberg-atom sensors, paving the way for next-generation, high-sensitivity monitoring and evaluation systems in navigation and timing infrastructure.