Radio Frequency Fingerprinting (RFF) is a promising technique for physical-layer hardware identification. Among various hardware-induced features, nonlinear distortions introduced by power amplifiers (PAs) contribute significantly to the overall RFF. However, fingerprint components related to PA behavior are sensitive to PA module replacement, variations in transmit power, and their coupling with multipath wireless channels, which can degrade identification performance in practical scenarios. To address these challenges, we propose a unified system model that jointly models and compensates for both PA nonlinear distortions and wireless channel convolution effects. Building on this model, we develop a Half-Quadratic Splitting (HQS)-based alternating optimization strategy to iteratively estimate the channel matrix and PA nonlinear coefficients. Experiments on real-world LoRa datasets show that the proposed method achieves robust identification performance: 95.22% accuracy under LOS and 91.19% under NLOS conditions when tested against unseen PA modules, and 97.50%(LOS) and 90.78%(NLOS) accuracy under varying transmit power levels.