I know I can click Project > Add Folder and achieve the same, but the behavior is kind of odd for my use and I'm just not used to it even after a year of using ST.
Does anyone know if I can force similar behavior for File > Open ?
Projects work with folders not individual files, so exactly what you want isn't available. Perhaps you could get something similar to work if you create a plugin that will add some file to a project folder. This project folder could contain symlinks to the actual files.