Automatic Speech Recognition (ASR) can significantly reduce documentation burden in clinical workflows, but standard models degrade sharply in real-world telephony settings where noisy audio, dialectal variation, and strict data residency constraints prevent cloud-based adaptation. We study this "reality gap" using Gram Vaani: a telephonic Hindi corpus spanning rural healthcare and agricultural helplines, as the closest available proxy for clinical speech under strict on-device constraints. We show that a robust multilingual model (IndicWav2Vec) degrades from 11.59\% WER on standard clean Hindi to \textbf{41.71\% WER} on this proxy telephony data. We evaluate a progression of on-device adaptation regimes under realistic constraints, from full fine-tuning to parameter-efficient LoRA and stream-based continual learning, across multiple baselines, datasets, and seeds. Focusing on continual learning, our central finding highlights a critical interaction between Experience Replay (ER) and Elastic Weight Consolidation (EWC, parameterized by regularization strength $λ$). We show that standard positive EWC ($λ> 0$) can oppose replay-driven updates, limiting adaptation. Reversing EWC's strength ($λ< 0$) suggests that it can act as a directional control signal under ER-guided adaptation: negative $λ$ reinforces replay-driven plasticity, while a scheduled $λ$ enables phase-dependent control of stability and plasticity. Across evaluations on multiple datasets, we find that multi-domain replay provides a strong foundation for adaptation, while EWC modulates stability-plasticity dynamics without altering final performance. These results show that effective on-device adaptation depends on understanding how data-driven and parameter-level learning signals interact, rather than choosing methods in isolation.