Spine surgery is a high-risk intervention demanding precise execution, often supported by image-based navigation systems. Recently, supervised learning approaches have gained attention for reconstructing 3D spinal anatomy from sparse fluoroscopic data, significantly reducing reliance on radiation-intensive 3D imaging systems. However, these methods typically require large amounts of annotated training data and may struggle to generalize across varying patient anatomies or imaging conditions. Instance-learning approaches like Gaussian splatting could offer an alternative by avoiding extensive annotation requirements. While Gaussian splatting has shown promise for novel view synthesis, its application to sparse, arbitrarily posed real intraoperative X-rays has remained largely unexplored. This work addresses this limitation by extending the $R^2$-Gaussian splatting framework to reconstruct anatomically consistent 3D volumes under these challenging conditions. We introduce an anatomy-guided radiographic standardization step using style transfer, improving visual consistency across views, and enhancing reconstruction quality. Notably, our framework requires no pretraining, making it inherently adaptable to new patients and anatomies. We evaluated our approach using an ex-vivo dataset. Expert surgical evaluation confirmed the clinical utility of the 3D reconstructions for navigation, especially when using 20 to 30 views, and highlighted the standardization's benefit for anatomical clarity. Benchmarking via quantitative 2D metrics (PSNR/SSIM) confirmed performance trade-offs compared to idealized settings, but also validated the improvement gained from standardization over raw inputs. This work demonstrates the feasibility of instance-based volumetric reconstruction from arbitrary sparse-view X-rays, advancing intraoperative 3D imaging for surgical navigation.