Diffuse optics has the potential to offer a substantial advancement in fetal health monitoring via enabling continuous measurement of fetal blood oxygen saturation (fSpO$_2$). Aiming to enhance the sensing accuracy and to elucidate the foundational limits of Transabdominal Fetal Oximetry (TFO) via diffuse optics, we introduce a theoretical derivation, and a comprehensive pipeline for fSpO$_2$ estimation from non-invasively sensed diffuse light intensity values, which are leveraged to analyze datasets obtained through both simulations and in-vivo experiments in gold standard large animal model of pregnancy. We propose the Exponential Pulsation Ratio (EPR) as a key feature, and develop machine-learning models to fuse the information collected across multiple detectors. Our proposed method demonstrates a Mean Absolute Error (MAE) of 4.81% and 6.85% with a Pearson's r correlation of 0.81 (p<0.001) and 0.71 (p<0.001) for estimation of fSpO$_2$ in simulated dataset and in-vivo dataset, respectively. Across both datasets, our method outperforms the existing approaches, enhancing the accuracy of the fSpO$_2$ estimation and demonstrates its viability as a supplemental technology for intrapartum fetal monitoring.