Thorium-227-based alpha-particle radiopharmaceutical therapies ({\alpha}-RPTs) are being investigated in several clinical and pre-clinical studies. After administration, Thorium-227 decays to Radium-223, another alpha-particle-emitting isotope, which redistributes within the patient. Reliable dose quantification of both Thorium-227 and Radium-223 is clinically important, and SPECT may perform this quantification as these isotopes also emit X- and gamma-ray photons. However, reliable quantification is challenged by the orders-of-magnitude lower activity compared to conventional SPECT, resulting in a very low number of detected counts, the presence of multiple photopeaks, substantial overlap in the emission spectra of these isotopes, and the image-degrading effects in SPECT. To address these issues, we propose a multiple-energy-window projection-domain quantification (MEW-PDQ) method that jointly estimates the regional activity uptake of both Thorium-227 and Radium-223 directly using the SPECT projection from multiple energy windows. We evaluated the method with realistic simulation studies using anthropomorphic digital phantoms, in the context of imaging patients with bone metastases of prostate cancer and treated with Thorium-227-based {\alpha}-RPTs. The proposed method yielded reliable (accurate and precise) regional uptake estimates of both isotopes and outperformed state-of-the-art methods across different lesion sizes and contrasts, in a virtual imaging trial, as well as with moderate levels of intra-regional heterogeneous uptake and with moderate inaccuracies in the definitions of the support of various regions. Additionally, we demonstrated the effectiveness of using multiple energy windows and the variance of the estimated uptake using the proposed method approached the Cram\'er-Rao-lower-bound-defined theoretical limit.