Your balance and low and deep stances mean next to nothing unless your feet are deep into your opponent's personal space. Hold the foot fetish imagery for a second and consider the "why." Surely there must have been a reason for emphasizing deep stances and footwork, even if the old karate masters could not explain why?
In the attached video, chief SSBD instructor Maul Mornie demonstrates a thigh sweep, which might trigger an "a-ha!" moment. In order to perform this technique correctly you must step through your opponent side-on. As you do, your thigh, close to the inguinal crease, clips your opponent's leg and throws him off balance. Like anything, it takes practice.
Maul performs this throw (Simbur) effortlessly, which comes from walking through countless opponents. You cannot develop this skill with thousands of repetitions against your reflection in a mirror. As you watch the video, you might notice that the technique looks a bit like kiba dachi, and at other times, like zenkutsu dachi or kokotsu dachi. That's okay. Naming something is an act of taking possession, but if you do not understand what you are taking hold of, the name hardly matters. Forget the names for a moment and just do.
When you train with Maul, as I do, naturally you become more adept in the art of SSBD, as a side bonus for karateka, it makes your karate better.