You're going to have to train in it a bit to see it and be able to appreciate what is going on...it has the subtleties of any koryu.
There are countless variations that revolve around a few principles. There is not going to be one single answer for every single question.
As for the one handed techniques, why would any koryu sword practitioner go with one hand in a particular instant of an encounter...distance.
In regards to what the other hand is doing, Okinawan guards/ Udundi practitioners carry the sword out of the obi. Practice is ambidextrous. The saya is in the other hand. Udundi Iai uses the same concept as bringing the tsuka forward on approach and then applying sayabiki to advance the timing of the draw. Only, the draw and reach is not limited to the saya being in the belt, the sword can completely be moved towards the opponent, or anywhere for that matter, and then the saya stripped off the sword.
Motobu Udundi is an intense study of ma ai and ashi sabaki. As with any koryu, a certain degree of commitment to it has to happen in order to appreciate it.
Rob Rivers