Left panel: J1753 spectra showing the BAs evolution during its 2023 outburst, zoomed into the Balmer $\mathrm{H}\delta$, $\mathrm{H}\gamma$, and $\mathrm{H}\beta$ transitions. The colour of the spectra corresponds to the X-ray spectral state, following the same convention as in Fig. C.1. The best fit corresponding with the parameters shown in the right panel is shown as a solid blue line. The rest wavelength of the transition is marked with a dashed black line, while blue-dotted lines mark velocity shifts of $\pm 2500\mathrm{km}{\mathrm{s}}^{-1}$ as a visual reference. Black regions of the spectra were masked during the fit due to the presence of a telluric band. Right panel: Best fitting parameters for the spectroscopic sample of J1357, following the same description as in Fig. C.2.