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Over the last two decades, around 300 quasars have been discovered at $z\gtrsim6$, yet only one has identified as being strongly gravitationally lensed. We explore a new approach -- enlarging the permitted spectral parameter space, while introducing a new spatial geometry veto criterion -- which is implemented via image-based deep learning. We first apply this approach to a systematic search for reionization-era lensed quasars, using data from the Dark Energy Survey, the Visible and Infrared Survey Telescope for Astronomy Hemisphere Survey, and the Wide-field Infrared Survey Explorer.Our search method consists of two main parts: (i) the preselection of the candidates based on their spectral energy distributions (SEDs) using catalog-level photometry and (ii) relative probabilities calculation of the candidates being a lens or some contaminant, utilizing a convolutional neural network (CNN) classification. The training data sets are constructed by painting deflected point-source lights over actual galaxy images, to generate realistic galaxy-quasar lens models, optimized to find systems with small image separations, i.e., Einstein radii of $θ_\mathrm{E} \leq 1$ arcsec. Visual inspection is then performed for sources with CNN scores of $P_\mathrm{lens} > 0.1$, which leads us to obtain 36 newly selected lens candidates, which are awaiting spectroscopic confirmation. These findings show that automated SED modeling and deep learning pipelines, supported by modest human input, are a promising route for detecting strong lenses from large catalogs that can overcome the veto limitations of primarily dropout-based SED selection approaches.