Traumatic brain injury (TBI) is a major cause of death and disability. The current front-line imaging modality for TBI detection is CT, which reliably detects intracranial hemorrhage (fresh blood contrast 30-50 HU, size down to 1 mm) in non-contrast-enhanced exams. Compared to CT, flat-panel detector (FPD) cone-beam CT (CBCT) systems offer lower cost, greater portability, and smaller footprint suitable for point-of-care deployment. We are developing FPD-CBCT to facilitate TBI detection at the point-of-care such as in emergent, ambulance, sports, and military applications. However, current FPD-CBCT systems generally face challenges in low-contrast, soft-tissue imaging. Model-based reconstruction can improve image quality in soft-tissue imaging compared to conventional filtered back-projection (FBP) by leveraging high-fidelity forward model and sophisticated regularization. In FPD-CBCT TBI imaging, measurement noise characteristics undergo substantial change following artifact correction, resulting in non-negligible noise amplification. In this work, we extend the penalized weighted least-squares (PWLS) image reconstruction to include the two dominant artifact corrections (scatter and beam hardening) in FPD-CBCT TBI imaging by correctly modeling the variance change following each correction. Experiments were performed on a CBCT test-bench using an anthropomorphic phantom emulating intra-parenchymal hemorrhage in acute TBI, and the proposed method demonstrated an improvement in blood-brain contrast-to-noise ratio (CNR = 14.2) compared to FBP (CNR = 9.6) and PWLS using conventional weights (CNR = 11.6) at fixed spatial resolution (1 mm edge-spread width at the target contrast). The results support the hypothesis that FPD-CBCT can fulfill the image quality requirements for reliable TBI detection, using high-fidelity artifact correction and statistical reconstruction with accurate post-artifact-correction noise models.