The dual-energy computed tomography (DECT)-based approach holds promise in reducing the overall uncertainty in proton stopping-power-ratio (SPR) estimation, but cannot be easily implemented with most commercial proton treatment planning systems (TPS). In this study, we revisited the idea of coupling the stoichiometric calibration method with virtual monoenergetic CT datasets (MonoCT) generated by modern DECT scanners, because of its readiness for implementation with the existing TPS. Our objective was to determine the optimal energy of the MonoCT dataset for stoichiometric calibration and estimate the overall uncertainty in SPR estimation at the optimal energy. We performed stoichiometric calibration for MonoCT datasets across the energy range available on a Siemens Force DECT scanner and a Philips IQon DECT scanner in a 10 keV step. We estimated the uncertainties of different sources (imaging, modeling, and inherent uncertainties) for different tissue types (lung, soft, and bone tissues) associated with each energy; these were then combined into a single composite uncertainty for three tumor sites (head-and-neck (HN), lung, and prostate). The optimal energy was eventually selected based on the composite range uncertainty, which turned out to be 160 keV for both DECT scanners. At 160 keV, the total uncertainties (2σ) in SPR estimation were determined to be 3.2%-4.5%, 0.9%, and 1.4%-1.6% for lung, soft, and bony tissues, respectively. These results were comparable to the corresponding values estimated for the DECT approach evaluated in our previous study: 3.8%, 1.2% and 2.0%, for lung, soft, and bony tissues, respectively. The composite range uncertainties (2σ) were estimated as 1.5%, 1.7%, and 1.5% for prostate, lung, and HN, respectively. Our results demonstrated the potential of MonoCT images for reducing proton SPR uncertainty. Further clinical studies are needed to compare this approach with the DECT approach directly on real patient cases.