Fiber Bragg grating (FBG) sensors applying time-delay interrogators with wavelength swept lasers (WSLs) are popular for their great potentials in high sensing resolution and power budget. In these systems, well-calibrated WSLs with reduced wavelength nonlinearity and jitter are critical for the sensing performance. However, high-performance WSLs are expensive and could significantly increase the cost of the systems. The overall cost may be reduced by maximally sharing each WSL with multiple sensing FBGs through mechanisms like power splitting, which distribute the WSL signal into multiple independently operated serial FBG chains. Under such scenarios, the sensing processing unit (SPU) of each serial FBG chain must be synchronized with the WSL for correctly estimating the FBGs' respective spectra from the signal return time delays. We previously propose a self-synchronized scheme relying on the dual-polarity spectrum signal, which reduces the synchronization labor. The dual-polarity signal has a wider dynamic range, which may limit the system response speed or accuracy, considering the amplifiers' responses or the analog-to-digital converters' (ADCs') quantization noise. In this Letter, we apply peak-saturated FBG spectra for the sensors to increase the receivers' equivalent dynamic range. The flattop waveforms of the saturated peaks result in uncertainty for the peak positions. An artificial neutral network (ANN)-based method is further studied to enhance the peak detection accuracy. We show an ∼88% receiver dynamic range improvement with an inaccuracy reduction of about a half compared to the filter-and-maximum-readout (FMR) method.