Purpose: T2* quantification from gradient echo magnetic resonance imaging is particularly affected by subject motion due to the high sensitivity to magnetic field inhomogeneities, which are influenced by motion and might cause signal loss. Thus, motion correction is crucial to obtain high-quality T2* maps. Methods: We extend our previously introduced learning-based physics-informed motion correction method, PHIMO, by utilizing acquisition knowledge to enhance the reconstruction performance for challenging motion patterns and increase PHIMO's robustness to varying strengths of magnetic field inhomogeneities across the brain. We perform comprehensive evaluations regarding motion detection accuracy and image quality for data with simulated and real motion. Results: Our extended version of PHIMO outperforms the learning-based baseline methods both qualitatively and quantitatively with respect to line detection and image quality. Moreover, PHIMO performs on-par with a conventional state-of-the-art motion correction method for T2* quantification from gradient echo MRI, which relies on redundant data acquisition. Conclusion: PHIMO's competitive motion correction performance, combined with a reduction in acquisition time by over 40% compared to the state-of-the-art method, make it a promising solution for motion-robust T2* quantification in research settings and clinical routine.