We present SpINRv2, a neural framework for high-fidelity volumetric reconstruction using Frequency-Modulated Continuous-Wave (FMCW) radar. Extending our prior work (SpINR), this version introduces enhancements that allow accurate learning under high start frequencies-where phase aliasing and sub-bin ambiguity become prominent. Our core contribution is a fully differentiable frequency-domain forward model that captures the complex radar response using closed-form synthesis, paired with an implicit neural representation (INR) for continuous volumetric scene modeling. Unlike time-domain baselines, SpINRv2 directly supervises the complex frequency spectrum, preserving spectral fidelity while drastically reducing computational overhead. Additionally, we introduce sparsity and smoothness regularization to disambiguate sub-bin ambiguities that arise at fine range resolutions. Experimental results show that SpINRv2 significantly outperforms both classical and learning-based baselines, especially under high-frequency regimes, establishing a new benchmark for neural radar-based 3D imaging.