A really terrible job is being made explaining everything here.
The whole point of Sinbad's plan resides on the magic formula made by Ugo, that made David completely and utterly aghast at at his achievements after his failed attempt gaining control as God.
After Elder David infiltrates the Sacred Palace, takes over it and yeets Ugo out, he is restrained right away by Ugo once more, and left helpless. Extremely confused, he asks what the hell is happening, to which Ugo explains that this is a result of his curiosity and too much free time, where he found out a way to trade ranks in the infinitely rising hierarchy of Gods. Ugo used this to, in his own words, become a God that exceeded God and take control back from Elder David. As further proof of this, when Arba awakes on the Sacred Palace and asks for Ill Illah and Elder David, he points to Ill Illah and David making a "lower order world" in a small fish tank, with its own cosmos with life.
Rather, Ugo had already stated since before this accident that he was a dimensional level above the magi universe, so he became one level higher than his previous level when David took over the Sacred Palace and Ugo stopped him by becoming superior once more. Sinbad only stops him from interfering because he's incredibly mentally broken and David makes an illusion of Solomon to keep him out of the way,
Using the rukh of the whole world, as I can remember, isn't necessary. It is just something Sinbad wanted to do for his own desires.